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• Quasi-Experimental Design | Definition, Types & Examples

Quasi-Experimental Design | Definition, Types & Examples

Published on July 31, 2020 by Lauren Thomas . Revised on January 22, 2024.

Like a true experiment , a quasi-experimental design aims to establish a cause-and-effect relationship between an independent and dependent variable .

However, unlike a true experiment, a quasi-experiment does not rely on random assignment . Instead, subjects are assigned to groups based on non-random criteria.

Quasi-experimental design is a useful tool in situations where true experiments cannot be used for ethical or practical reasons.

Table of contents

Differences between quasi-experiments and true experiments, types of quasi-experimental designs, when to use quasi-experimental design, advantages and disadvantages, other interesting articles, frequently asked questions about quasi-experimental designs.

There are several common differences between true and quasi-experimental designs.

Example of a true experiment vs a quasi-experiment

However, for ethical reasons, the directors of the mental health clinic may not give you permission to randomly assign their patients to treatments. In this case, you cannot run a true experiment.

Instead, you can use a quasi-experimental design.

You can use these pre-existing groups to study the symptom progression of the patients treated with the new therapy versus those receiving the standard course of treatment.

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Many types of quasi-experimental designs exist. Here we explain three of the most common types: nonequivalent groups design, regression discontinuity, and natural experiments.

Nonequivalent groups design

In nonequivalent group design, the researcher chooses existing groups that appear similar, but where only one of the groups experiences the treatment.

In a true experiment with random assignment , the control and treatment groups are considered equivalent in every way other than the treatment. But in a quasi-experiment where the groups are not random, they may differ in other ways—they are nonequivalent groups .

When using this kind of design, researchers try to account for any confounding variables by controlling for them in their analysis or by choosing groups that are as similar as possible.

This is the most common type of quasi-experimental design.

Regression discontinuity

Many potential treatments that researchers wish to study are designed around an essentially arbitrary cutoff, where those above the threshold receive the treatment and those below it do not.

Near this threshold, the differences between the two groups are often so minimal as to be nearly nonexistent. Therefore, researchers can use individuals just below the threshold as a control group and those just above as a treatment group.

However, since the exact cutoff score is arbitrary, the students near the threshold—those who just barely pass the exam and those who fail by a very small margin—tend to be very similar, with the small differences in their scores mostly due to random chance. You can therefore conclude that any outcome differences must come from the school they attended.

Natural experiments

In both laboratory and field experiments, researchers normally control which group the subjects are assigned to. In a natural experiment, an external event or situation (“nature”) results in the random or random-like assignment of subjects to the treatment group.

Even though some use random assignments, natural experiments are not considered to be true experiments because they are observational in nature.

Although the researchers have no control over the independent variable , they can exploit this event after the fact to study the effect of the treatment.

However, as they could not afford to cover everyone who they deemed eligible for the program, they instead allocated spots in the program based on a random lottery.

Although true experiments have higher internal validity , you might choose to use a quasi-experimental design for ethical or practical reasons.

Sometimes it would be unethical to provide or withhold a treatment on a random basis, so a true experiment is not feasible. In this case, a quasi-experiment can allow you to study the same causal relationship without the ethical issues.

The Oregon Health Study is a good example. It would be unethical to randomly provide some people with health insurance but purposely prevent others from receiving it solely for the purposes of research.

However, since the Oregon government faced financial constraints and decided to provide health insurance via lottery, studying this event after the fact is a much more ethical approach to studying the same problem.

True experimental design may be infeasible to implement or simply too expensive, particularly for researchers without access to large funding streams.

At other times, too much work is involved in recruiting and properly designing an experimental intervention for an adequate number of subjects to justify a true experiment.

In either case, quasi-experimental designs allow you to study the question by taking advantage of data that has previously been paid for or collected by others (often the government).

Quasi-experimental designs have various pros and cons compared to other types of studies.

• Higher external validity than most true experiments, because they often involve real-world interventions instead of artificial laboratory settings.
• Higher internal validity than other non-experimental types of research, because they allow you to better control for confounding variables than other types of studies do.
• Lower internal validity than true experiments—without randomization, it can be difficult to verify that all confounding variables have been accounted for.
• The use of retrospective data that has already been collected for other purposes can be inaccurate, incomplete or difficult to access.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Ecological validity

Research bias

• Rosenthal effect
• Implicit bias
• Cognitive bias
• Selection bias
• Negativity bias
• Status quo bias

A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned.

In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.

Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment .

Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity  as they can use real-world interventions instead of artificial laboratory settings.

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Quasi Experimental Design Overview & Examples

By Jim Frost Leave a Comment

What is a Quasi Experimental Design?

A quasi experimental design is a method for identifying causal relationships that does not randomly assign participants to the experimental groups. Instead, researchers use a non-random process. For example, they might use an eligibility cutoff score or preexisting groups to determine who receives the treatment.

Quasi-experimental research is a design that closely resembles experimental research but is different. The term “quasi” means “resembling,” so you can think of it as a cousin to actual experiments. In these studies, researchers can manipulate an independent variable — that is, they change one factor to see what effect it has. However, unlike true experimental research, participants are not randomly assigned to different groups.

Learn more about Experimental Designs: Definition & Types .

When to Use Quasi-Experimental Design

Researchers typically use a quasi-experimental design because they can’t randomize due to practical or ethical concerns. For example:

• Practical Constraints : A school interested in testing a new teaching method can only implement it in preexisting classes and cannot randomly assign students.
• Ethical Concerns : A medical study might not be able to randomly assign participants to a treatment group for an experimental medication when they are already taking a proven drug.

Quasi-experimental designs also come in handy when researchers want to study the effects of naturally occurring events, like policy changes or environmental shifts, where they can’t control who is exposed to the treatment.

Quasi-experimental designs occupy a unique position in the spectrum of research methodologies, sitting between observational studies and true experiments. This middle ground offers a blend of both worlds, addressing some limitations of purely observational studies while navigating the constraints often accompanying true experiments.

A significant advantage of quasi-experimental research over purely observational studies and correlational research is that it addresses the issue of directionality, determining which variable is the cause and which is the effect. In quasi-experiments, an intervention typically occurs during the investigation, and the researchers record outcomes before and after it, increasing the confidence that it causes the observed changes.

However, it’s crucial to recognize its limitations as well. Controlling confounding variables is a larger concern for a quasi-experimental design than a true experiment because it lacks random assignment.

In sum, quasi-experimental designs offer a valuable research approach when random assignment is not feasible, providing a more structured and controlled framework than observational studies while acknowledging and attempting to address potential confounders.

Types of Quasi-Experimental Designs and Examples

Quasi-experimental studies use various methods, depending on the scenario.

Natural Experiments

This design uses naturally occurring events or changes to create the treatment and control groups. Researchers compare outcomes between those whom the event affected and those it did not affect. Analysts use statistical controls to account for confounders that the researchers must also measure.

Natural experiments are related to observational studies, but they allow for a clearer causality inference because the external event or policy change provides both a form of quasi-random group assignment and a definite start date for the intervention.

For example, in a natural experiment utilizing a quasi-experimental design, researchers study the impact of a significant economic policy change on small business growth. The policy is implemented in one state but not in neighboring states. This scenario creates an unplanned experimental setup, where the state with the new policy serves as the treatment group, and the neighboring states act as the control group.

Researchers are primarily interested in small business growth rates but need to record various confounders that can impact growth rates. Hence, they record state economic indicators, investment levels, and employment figures. By recording these metrics across the states, they can include them in the model as covariates and control them statistically. This method allows researchers to estimate differences in small business growth due to the policy itself, separate from the various confounders.

Nonequivalent Groups Design

This method involves matching existing groups that are similar but not identical. Researchers attempt to find groups that are as equivalent as possible, particularly for factors likely to affect the outcome.

For instance, researchers use a nonequivalent groups quasi-experimental design to evaluate the effectiveness of a new teaching method in improving students’ mathematics performance. A school district considering the teaching method is planning the study. Students are already divided into schools, preventing random assignment.

The researchers matched two schools with similar demographics, baseline academic performance, and resources. The school using the traditional methodology is the control, while the other uses the new approach. Researchers are evaluating differences in educational outcomes between the two methods.

They perform a pretest to identify differences between the schools that might affect the outcome and include them as covariates to control for confounding. They also record outcomes before and after the intervention to have a larger context for the changes they observe.

Regression Discontinuity

This process assigns subjects to a treatment or control group based on a predetermined cutoff point (e.g., a test score). The analysis primarily focuses on participants near the cutoff point, as they are likely similar except for the treatment received. By comparing participants just above and below the cutoff, the design controls for confounders that vary smoothly around the cutoff.

For example, in a regression discontinuity quasi-experimental design focusing on a new medical treatment for depression, researchers use depression scores as the cutoff point. Individuals with depression scores just above a certain threshold are assigned to receive the latest treatment, while those just below the threshold do not receive it. This method creates two closely matched groups: one that barely qualifies for treatment and one that barely misses out.

By comparing the mental health outcomes of these two groups over time, researchers can assess the effectiveness of the new treatment. The assumption is that the only significant difference between the groups is whether they received the treatment, thereby isolating its impact on depression outcomes.

Controlling Confounders in a Quasi-Experimental Design

Accounting for confounding variables is a challenging but essential task for a quasi-experimental design.

In a true experiment, the random assignment process equalizes confounders across the groups to nullify their overall effect. It’s the gold standard because it works on all confounders, known and unknown.

Unfortunately, the lack of random assignment can allow differences between the groups to exist before the intervention. These confounding factors might ultimately explain the results rather than the intervention.

Consequently, researchers must use other methods to equalize the groups roughly using matching and cutoff values or statistically adjust for preexisting differences they measure to reduce the impact of confounders.

A key strength of quasi-experiments is their frequent use of “pre-post testing.” This approach involves conducting initial tests before collecting data to check for preexisting differences between groups that could impact the study’s outcome. By identifying these variables early on and including them as covariates, researchers can more effectively control potential confounders in their statistical analysis.

Additionally, researchers frequently track outcomes before and after the intervention to better understand the context for changes they observe.

Statisticians consider these methods to be less effective than randomization. Hence, quasi-experiments fall somewhere in the middle when it comes to internal validity , or how well the study can identify causal relationships versus mere correlation . They’re more conclusive than correlational studies but not as solid as true experiments.

In conclusion, quasi-experimental designs offer researchers a versatile and practical approach when random assignment is not feasible. This methodology bridges the gap between controlled experiments and observational studies, providing a valuable tool for investigating cause-and-effect relationships in real-world settings. Researchers can address ethical and logistical constraints by understanding and leveraging the different types of quasi-experimental designs while still obtaining insightful and meaningful results.

Cook, T. D., & Campbell, D. T. (1979).  Quasi-experimentation: Design & analysis issues in field settings . Boston, MA: Houghton Mifflin

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Practical Guide to Experimental and Quasi-Experimental Research in Surgical Education

• 1 Department of Surgery, Massachusetts General Hospital, Harvard Medical School, Boston
• 2 Department of Biostatistics, Gillings School of Global Public Health, University of North Carolina at Chapel Hill
• 3 Statistical Editor, JAMA Surgery
• 4 Department of Surgery, Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts
• Editorial Improving the Integrity of Surgical Education Scholarship Amalia Cochran, MD, MA; Dimitrios Stefanidis, MD, PhD; Melina R. Kibbe, MD JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Survey Research in Surgical Education Adnan A. Alseidi, MD, EdM; Jason S. Haukoos, MD, MSc; Christian de Virgilio, MD JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Common Flaws With Surgical Education Research Dimitrios Stefanidis, MD, PhD; Laura Torbeck, PhD; Amy H. Kaji, MD, PhD JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Machine Learning and Artificial Intelligence in Surgical Education Research Daniel A. Hashimoto, MD; Julian Varas, MD; Todd A. Schwartz, DrPH JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Surgical Simulation Research Aimee K. Gardner, PhD; Amy H. Kaji, MD, PhD; Marja Boermeester, MD, PhD JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Qualitative Research in Surgical Education Gurjit Sandhu, PhD; Amy H. Kaji, MD, PhD; Amalia Cochran, MD, MA JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Assessment Tool Development for Surgical Education Research Mohsen M. Shabahang, MD, PhD; Todd A. Schwartz, DrPH; Liane S. Feldman, MD JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Pragmatic Clinical Trials in Surgical Education Research Karl Y. Bilimoria, MD, MS; Jason S. Haukoos, MD, MSc; Gerard M. Doherty, MD JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Ethics in Surgical Education Research Michael M. Awad, MD, PhD, MHPE; Amy H. Kaji, MD, PhD; Timothy M. Pawlik, MD, PhD, MTS, MPH, MBA JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Education Program Evaluation Research Marc de Moya, MD; Jason S. Haukoos, MD, MSc; Kamal M. F. Itani, MD JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Curricular Development Research Kevin Y. Pei, MD, MHS; Todd A. Schwartz, DrPH; Marja A. Boermeester, MD, PhD JAMA Surgery

Experimental and quasi-experimental study designs primarily stem from the positivism research paradigms, which argue that there is an objective truth to reality that can be discerned using the scientific method. 1 This hypothetico-deductive scientific model is a circular process that begins with a literature review to build testable hypotheses, experimental design that manipulates some variables and controls others, and then careful assessment and analysis of those effects to build further theories and experiments, before cycling through again. In 1963, Campbell and Stanley 2 categorically defined experimental education research as “that portion of research in which variables are manipulated and their effects upon other variables observed” p1 and quasi-experimental as education research “where random assignment to equivalent groups is not possible.” p2 Surgical education studies frequently must forego true randomization due to factors outside the researcher’s control. For example, medical students doing their surgery clerkship at the end of the year are not identical to the medical students on their surgical clerkship as their first rotation of the academic year. Therefore, for the rest of this guide, we will refer to both experimental and quasi-experimental study designs as experiments.

• Editorial Improving the Integrity of Surgical Education Scholarship JAMA Surgery

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Phitayakorn R , Schwartz TA , Doherty GM. Practical Guide to Experimental and Quasi-Experimental Research in Surgical Education. JAMA Surg. 2024;159(5):578–579. doi:10.1001/jamasurg.2023.6693

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• Published: 11 February 2021

Conceptualising natural and quasi experiments in public health

• Frank de Vocht   ORCID: orcid.org/0000-0003-3631-627X 1 , 2 , 3 ,
• Srinivasa Vittal Katikireddi 4 ,
• Cheryl McQuire 1 , 2 ,
• Kate Tilling 1 , 5 ,
• Matthew Hickman 1 &
• Peter Craig 4  

BMC Medical Research Methodology volume  21 , Article number:  32 ( 2021 ) Cite this article

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Natural or quasi experiments are appealing for public health research because they enable the evaluation of events or interventions that are difficult or impossible to manipulate experimentally, such as many policy and health system reforms. However, there remains ambiguity in the literature about their definition and how they differ from randomized controlled experiments and from other observational designs. We conceptualise natural experiments in the context of public health evaluations and align the study design to the Target Trial Framework.

A literature search was conducted, and key methodological papers were used to develop this work. Peer-reviewed papers were supplemented by grey literature.

Natural experiment studies (NES) combine features of experiments and non-experiments. They differ from planned experiments, such as randomized controlled trials, in that exposure allocation is not controlled by researchers. They differ from other observational designs in that they evaluate the impact of events or process that leads to differences in exposure. As a result they are, in theory, less susceptible to bias than other observational study designs. Importantly, causal inference relies heavily on the assumption that exposure allocation can be considered ‘as-if randomized’. The target trial framework provides a systematic basis for evaluating this assumption and the other design elements that underpin the causal claims that can be made from NES.

Conclusions

NES should be considered a type of study design rather than a set of tools for analyses of non-randomized interventions. Alignment of NES to the Target Trial framework will clarify the strength of evidence underpinning claims about the effectiveness of public health interventions.

Peer Review reports

When designing a study to estimate the causal effect of an intervention, the experiment (particularly the randomised controlled trial (RCT) is generally considered to be the least susceptible to bias. A defining feature of the experiment is that the researcher controls the assignment of the treatment or exposure. If properly conducted, random assignment balances unmeasured confounders in expectation between the intervention and control groups . In many evaluations of public health interventions, however, it is not possible to conduct randomised experiments. Instead, standard observational epidemiological study designs have traditionally been used. These are known to be susceptible to unmeasured confounding.

Natural experimental studies (NES) have become popular as an alternative evaluation design in public health research, as they have distinct benefits over traditional designs [ 1 ]. In NES, although the allocation and dosage of treatment or exposure are not under the control of the researcher, they are expected to be unrelated to other factors that cause the outcome of interest [ 2 , 3 , 4 , 5 ]. Such studies can provide strong causal information in complex real-world situations, and can generate effect sizes close to the causal estimates from RCTs [ 6 , 7 , 8 ]. The term natural experiment study is sometimes used synonymously with quasi-experiment; a much broader term that can also refer to researcher-led but non-randomised experiments. In this paper we argue for a clearer conceptualisation of natural experiment studies in public health research, and present a framework to improve their design and reporting and facilitate assessment of causal claims.

Natural and quasi-experiments have a long history of use for evaluations of public health interventions. One of the earliest and best-known examples is the case of ‘Dr John Snow and the Broad Street pump’ [ 9 ]. In this study, cholera deaths were significantly lower among residents served by the Lambeth water company, which had moved its intake pipe to an upstream location of the Thames following an earlier outbreak, compared to those served by the Southwark and Vauxhall water company, who did not move their intake pipe. Since houses in the study area were serviced by either company in an essentially random manner, this natural experiment provided strong evidence that cholera was transmitted through water [ 10 ].

Natural and quasi experiments

Natural and quasi experiments are appealing because they enable the evaluation of changes to a system that are difficult or impossible to manipulate experimentally. These include, for example, large events, pandemics and policy changes [ 7 , 11 ]. They also allow for retrospective evaluation when the opportunity for a trial has passed [ 12 ]. They offer benefits over standard observational studies because they exploit variation in exposure that arises from an exogenous ( i.e. not caused by other factors in the analytic model [ 1 ]) event or intervention. This aligns them to the ‘ do -operator’ in the work of Pearl [ 13 ]. Quasi experiments (QES) and NES thus combine features of experiments (exogenous exposure) and non-experiments (observations without a researcher-controlled intervention). As a result, they are generally less susceptible to confounding than many other observational study designs [ 14 ]. However, a common critique of QES and NES is that because the processes producing variation in exposure are outside the control of the research team, there is uncertainty as to whether confounding has been sufficiently minimized or avoided [ 7 ]. For example, a QES of the impact of a voluntary change by a fast food chain to label its menus with information on calories on subsequent purchasing of calories [ 15 ]. Unmeasured differences in the populations that visit that particular chain compared to other fast-food choices could lead to residual confounding.

A distinction is sometimes made between QES and NES. The term ‘natural experiment’ has traditionally referred to the occurrence of an event with a natural cause; a ‘force of nature‘(Fig.  1 a) [ 1 ]. These make for some of the most compelling studies of causation from non-randomised experiments. For example, the Canterbury earthquakes in 2010–2011 have been used to study the causal impact of such disasters because about half of an established birth cohort lived in the affected area with the remainder of the cohort living elsewhere [ 16 ]. More recently, the use of the term ‘natural’ has been understood more broadly as an event which did not involve the deliberate manipulation of exposure for research purposes (for example a policy change), even if human agency was involved [ 17 ]. Compared to natural experiments in QES the research team may be able to influence exposure allocation, even if the event or exposure itself is not under their full control; for example in a phased roll out of a policy [ 18 ]. A well-known example of a natural experiment is the “Dutch Hunger Winter” summarised by Lumey et al. [ 19 ]. During this period in the Second World War the German authorities blocked all food supplies to the occupied West of the Netherlands, which resulted in widespread starvation. Food supplies were restored immediately after the country was liberated, so the exposure was sharply defined by time as well as place. Because there was sufficient food in the occupied and liberated areas of the Netherlands before and after the Hunger Winter, exposure to famine occurred based on an individual’s time and place (of birth) only. Similar examples of such ‘political’ natural experiment studies are the study of the impact of China’s Great Famine [ 20 ] and the ‘special period’ in Cuba’s history following the collapse of the Soviet Union and the imposition of a US blockade [ 21 ]. NES that describe the evaluation of an event which did not involve the deliberate manipulation of an exposure but involved human agency, such as the impact of a new policy, are the mainstay of ‘natural experimental research’ in public health, and the term NES has become increasingly popular to indicate any quasi-experimental design (although it has not completely replaced it).

Different conceptualisations of natural and quasi experiments within wider evaluation frameworks

Dunning takes the distinction of a NES further. He defines a NES as a QES where knowledge about the exposure allocation process provides a strong argument that allocation, although not deliberately manipulated by the researcher, is essentially random. This concept is referred to as ‘as-if randomization’ (Fig. 1 b) [ 4 , 8 , 10 ]. Under this definition, NES differ from QES in which the allocation of exposure, whether partly controlled by the researcher or not, does not clearly resemble a random process.

A third distinction between QES and NES has been made that argues that NES describe the study of unplanned events whereas QES describe evaluations of events that are planned (but not controlled by the researcher), such as policies or programmes specifically aimed at influencing an outcome (Fig. 1 c) [ 17 ]. In practice however, the distinction between these can be ambiguous.

When the assignment of exposure is not controlled by the researcher, with rare exceptions (for example lottery-system [ 22 ] or military draft [ 23 ] allocations), it is typically very difficult to prove that true (as-if) randomization occurred. Because of the ambiguity of ‘as-if randomization’ and the fact that the tools to assess this are the same as those used for assessment of internal validity in any observational study [ 12 ], the UK Medical Research Council (MRC) guidance advocates a broader conceptualisation of a NES. Under the MRC guidance, a NES is defined as any study that investigates an event that is not under the control of the research team, and which divides a population into exposed and unexposed groups, or into groups with different levels of exposure (Fig. 1 d).

Here, while acknowledging the remaining ambiguity regarding the precise definition of a NES, in consideration of the definitions above [ 24 ], we argue that:

what distinguishes NES from RCTs is that allocation is not controlled by the researchers and;

what distinguishes NES from other observational designs is that they specifically evaluate the impact of a clearly defined event or process which result in differences in exposure between groups.

A detailed assessment of the allocation mechanism (which determines exposure status) is essential. If we can demonstrate that the allocation process approximates a randomization process, any causal claims from NES will be substantially strengthened. The plausibility of the ‘as-if random’ assumption strongly depends on detailed knowledge of why and how individuals or groups of individuals were assigned to conditions and how the assignment process was implemented [ 10 ]. This plausibility can be assessed quantitatively for observed factors using standard tools for assessment of internal validity of a study [ 12 ], and should ideally be supplemented by a qualitative description of the assignment process. Common with contemporary public health practice, we will use the term ‘natural experiment study’, or NES to refer to both NES and QES, from hereon.

Medline, Embase and Google Scholar were searched using search terms including quasi-experiment, natural experiment, policy evaluation and public health evaluation and key methodological papers were used to develop this work. Peer-reviewed papers were supplemented by grey literature.

Part 1. Conceptualisations of natural experiments

An analytic approach.

Some conceptualisations of NES place their emphasis on the analytic tools that are used to evaluate natural experiments [ 25 , 26 ]. In this conceptualisation NES are understood as being defined by the way in which they are analysed, rather than by their design. An array of different statistical methods is available to analyse natural experiments, including regression adjustments, propensity scores, difference-in-differences, interrupted time series, regression discontinuity, synthetic controls, and instrumental variables. Overviews including strengths and limitations of the different methods are provided in [ 12 , 27 ]. However, an important drawback of this conceptualisation is that it suggests that there is a distinct set of methods for the analysis of NES.

A study design

The popularity of NES has resulted in some conceptual stretching, where the label is applied to a research design that only implausibly meets the definitional features of a NES [ 10 ]. For example, observational studies exploring variation in exposures (rather than the study of an event or change in exposure) have sometimes also been badged as NES. A more stringent classification of NES as a type of study design, rather than a collection of analytic tools, is important because it prevents attempts to incorrectly cover observational studies with a ‘glow of experimental legitimacy’ [ 10 ]. If the design rather than the statistical methodology defines a NES, this allows an open-ended array of statistical tools. These tools are not necessarily constrained by those mentioned above, but could also, for example, include new methods such as synthetic controls that can be utilised to analyse the natural experiments. The choice of appropriate evaluation method should be based on what is most suitable for each particular study, and then depends on the knowledge about the event, the availability of data, and design elements such as its allocation process.

Dunning argues that it is the overall research design, rather than just the statistical methods, that compels conviction when making causal claims. He proposes an evaluation framework for NES along the three dimensions of (1) the plausibility of as-if randomization of treatment, (2) the credibility of causal and statistical models, and (3) the substantive relevance of the treatment. Here, the first dimension is considered key for distinguishing NES from other QES [ 4 ]. NES can be divided into those where a plausible case for ‘as-if random’ assignment can be made (which he defines as NES), and those where confounding from observed factors is directly adjusted for through statistical means. The validity of the latter (which Dunning defines as ‘other quasi experiments’, and we define as ‘weaker NES’) relies on the assumption that unmeasured confounding is absent [ 8 ], and is considered less credible in theory for making causal claims [ 4 ]. In this framework, the ‘as-if-randomised’ NES can be viewed as offering stronger causal evidence than other quasi-experiments. In principle, they offer an opportunity for direct estimates of effects (akin to RCTs) where control for confounding factors would not necessarily be required [ 4 ], rather than relying on adjustment to derive conditional effect estimates [ 10 ]. Of course, the latter may well reach valid and compelling conclusions as well, but causal claims suffer to a higher degree from the familiar threats of bias and unmeasured confounding.

Part 2. A target trial framework for natural experiment studies

In this section, we provide recommendations for evaluation of the ‘as if random’ assumption and provide a unifying Target Trial Framework for NES, which brings together key sets of criteria that can be used to appraise the strength of causal claims from NES and assist with study design and reporting.

In public health, there is considerable overlap between analytic and design-based uses of the term NES. Nevertheless, we argue that if we consider NES a type of study design, causal inference can be strengthened by clear appraisal of the likelihood of ‘as-if’ random allocation of exposure. This should be demonstrated by both empirical evidence and by knowledge and reasoning about the causal question and substantive domain under question [ 8 , 10 ]. Because the concept of ‘as-if’ randomization is difficult, if not impossible to prove, it should be thought of along a ‘continuum of plausibility’ [ 10 ]. Specifically, for claims of ‘as-if’ randomization to be plausible, it must be demonstrated that the variables that determine treatment assignment are exogenous. This means that they are: i) strongly correlated with treatment status but are not caused by the outcome of interest (i.e. no reverse causality) and ii) independent of any other (measured or unmeasured) causes of the outcome of interest [ 8 ].

Given this additional layer of justification, especially with respect to the qualitative knowledge of the assignment process and domain knowledge from practitioners more broadly, we argue where feasible for the involvement of practitioners. This could, for example, be formalized through co-production in which members of the public and policy makers are involved in the development of the evaluation. If we appraise NES as a type of study design, which distinguish themselves from other designs because i) there is a particular change in exposure that is evaluated and ii) causal claims are supported by an argument of the plausibility of as-if randomization, then we guard against conflating NES with other observational designs [ 10 , 28 ].

There is a range of ways of dealing with the problems of selection on measured and unmeasured confounders in NES [ 8 , 10 ] which can be understood in terms of a ‘target trial’ we are trying to emulate, had randomization been possible [ 29 ]. The protocol of a target trial describes seven components common to RCTs (‘eligibility criteria’, ‘treatment strategies’, ‘assignment procedures’, ‘follow-up period’, ‘outcome’, ‘causal contrasts of interest’, and the ‘analysis plan’), and provides a systematic way of improving, reporting and appraising NES relative to a ‘gold standard’ (but often not feasible in practice) trial. In the design phase of a NES deviations from the target trial in each domain can be used to evaluate where improvements and where concessions will have to be made. This same approach can be used to appraise existing NES. The target trial framework also provides a structured way for reporting NES, which will facilitate evaluation of the strength of NES, improve consistency and completeness of reporting, and benefit evidence syntheses.

In Table  1 , we bring together elements of the Target Trial framework and conceptualisations of NES to derive a framework to describe the Target Trial for NES [ 12 ]. By encouraging researchers to address the questions in Table 1 , the framework provides a structured approach to the design, reporting and evaluation of NES across the seven target trial domains. Table 1 also provides recommendations to improve the strength of causal claims from NES, focussing primarily on sensitivity analyses to improve internal validity.

An illustrative example of a well-developed NES based on the criteria outlined in Table 1 is by Reeves et al. [ 39 ]. The NES evaluates the impact of the introduction of a National Minimum Wage on mental health. The study compared a clearly defined intervention group of recipients of a wage increase up to 110% of pre-intervention wage with clearly defined control groups of (1) people ineligible to the intervention because their wage at baseline was just above (100–110%) minimum wage and (2) people who were eligible, but whose companies did not comply and did not increase minimum wage. This study also included several sensitivity tests to strengthen causal arguments. We have aligned this study to the Target Trial framework in Additional file  1 .

The Target Trial Approach for NES (outlined in Table 1 ) provides a straightforward approach to improve, report, and appraise existing NES and to assist in the design of future studies. It focusses on structural design elements and goes beyond the use of quantitative tools alone to assess internal validity [ 12 ]. This work complements the ROBINS-I tool for assessing risk of bias in non-randomised studies of interventions, which similarly adopted the Target Trial framework [ 40 ]. Our approach focusses on the internal validity of a NES, with issues of construct and external validity being outside of the scope of this work (guidelines for these are provided in for example [ 41 ]). It should be acknowledged that less methodologically robust studies can still reach valid and compelling conclusions, even without resembling the notional target trial. However, we believe that drawing on the target trial framework helps highlight occasions when causal inference can be made more confidently.

And finally, the framework does explicitly exclude observational studies that aim to investigate the effects of changes in behaviour without an externally forced driver to do so. For example, although a cohort study can be the basis for the evaluation of a NES in principle, effects of the change of diet of some participants (compared to those who did not change their diet) is not an external cause (i.e. exogenous) and does not fall within the definition of an experiment [ 11 ]. However, such studies are likely to be more convincing than those which do not study within-person changes and we note that the statistical methods used may be similar to NES.

Despite their advantages, NES remain based on observational data and thus biases in assignment of the intervention can never be completely excluded (although for plausibly ‘as if randomised’ natural experiments these should be minimal). It is therefore important that a robust assessment of different potential sources of bias is reported. It has additionally been argued that sensitivity analyses are required to assess whether a pattern of small biases could explain away any ostensible effect of the intervention, because confidence intervals and statistical tests do not do this [ 14 ]. Recommendations that would improve the confidence with which we can make causal claims from NES, derived from work by Rosenbaum [ 14 ], have been outlined in Table 1 . Although sensitivity analyses can place plausible limits on the size of the effects of hidden biases, because such analyses are susceptible to assumptions about the maximum size of omitted biases, they cannot completely rule out residual bias [ 34 ]. Of importance for the strength of causal claims therefore, is the triangulation of NES with other evaluations using different data or study designs susceptible to different sources of bias [ 5 , 42 ].

None of the recommendations outlined in Table 1 will by themselves eliminate bias in a NES, but neither is it required to implement all of them to be able to make a causal claim with some confidence. Instead, a continuum of confidence in the causal claims based on the study design and the data is a more appropriate and practical approach [ 43 ]. Each sensitivity analysis aims to minimise ambiguity of a particular potential bias or biases, and as such a combination of selected sensitivity analyses can strengthen causal claims [ 14 ]. We would generally, but not strictly, consider a well conducted RCT as the design where we are most confident about such claims, followed by natural experiments, and then other observational studies; this would be an extension of the Grading of Recommendations Assessment, Development, and Evaluation (GRADE) framework [ 44 ]. GRADE provides a system for rating the quality (or certainty) of a body of evidence and grading the strength of recommendations for use in systematic reviews, health technology assessments (HTAs), and clinical practice guidelines. It typically only distinguishes between trials and observational studies when making these judgments (note however, that recent guidance does not make this explicit distinction when using ROBINS-I [ 45 ]). Given the increased contribution of NES in public health, especially those based on routine data [ 37 ], the specific inclusion of NES in this system might improve the rating of the evidence from these study designs.

Our recommendations are of particular importance for ensuring rigour in the context of (public) health research where natural experiments have become increasingly popular for a variety of reasons, including the availability of large routinely collected datasets [ 37 ]. Such datasets invite the discovery of natural experiments, even where the data may not be particularly applicable to this design, but also these enable many of the sensitivity analyses to be conducted from within the same dataset or through linkage to other routine datasets.

Finally, alignment to the Target Trial Framework also links natural experiment studies directly to other measures of trial validity, including pre-registration, reporting checklists, and evaluation through risk-of-bias-tools [ 40 ]. This aligns with previous recommendations to use established reporting guidelines such as STROBE, TREND [ 12 ], and TIDieR-PHP [ 46 ] for the reporting of natural experiment studies. These reporting guidelines could be customized to specific research areas (for example, as developed for a systematic review of quasi-experimental studies of prenatal alcohol use and birthweight and neurodevelopment [ 47 ]).

We provide a conceptualisation of natural experiment studies as they apply to public health. We argue for the appreciation of natural experiments as a type of study design rather than a set of tools for the analyses of non-randomised interventions. Although there will always remain some ambiguity about the strength of causal claims, there are clear benefits to harnessing NES rather than relying purely on observational studies. This includes the fact that NES can be based on routinely available data and that timely evidence of real-world relevance can be generated. The inclusion of a discussion of the plausibility of as-if randomization of exposure allocation will provide further confidence in the strength of causal claims.

Aligning NES to the Target Trial framework will guard against conceptual stretching of these evaluations and ensure that the causal claims about whether public health interventions ‘work’ are based on evidence that is considered ‘good enough’ to inform public health action within a ‘practice-based evidence’ framework. This framework describes how evaluations can help reducing critical uncertainties and adjust the compass bearing of existing policy (in contrast to the ‘evidence-based practice’ framework in which RCTs are used to generate ‘definitive’ evidence for particular interventions) [ 48 ].

Availability of data and materials

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Abbreviations

Randomised Controlled Trial

Natural Experiment

Stable Unit Treatment Value Assumption

Intention-To-Treat

Shadish WR, Cook TD, Campbell DT. Experimental and Quasi-Experimental Designs. 2nd ed. Wadsworth, Cengage Learning: Belmont; 2002.

Google Scholar  

King G, Keohane RO, Verba S. The importance of research Design in Political Science. Am Polit Sci Rev. 1995;89:475–81.

Article   Google Scholar  

Meyer BD. Natural and quasi-experiments in economics. J Bus Econ Stat. 1995;13:151–61.

Dunning T. Natural experiments in the social sciences. A design-based approach. 6th edition. Cambridge: Cambridge University Press; 2012.

Book   Google Scholar  

Craig P, Cooper C, Gunnell D, Haw S, Lawson K, Macintyre S, et al. Using natural experiments to evaluate population health interventions: new medical research council guidance. J Epidemiol Community Health. 2012;66:1182–6.

Cook TD, Shadish WR, Wong VC. Three conditions under which experiments and observational studies produce comparable causal estimates: new findings from within-study comparisons. J Policy Anal Manag. 2008;27:724–50.

Bärnighausen T, Røttingen JA, Rockers P, Shemilt I, Tugwell P. Quasi-experimental study designs series—paper 1: introduction: two historical lineages. J Clin Epidemiol. 2017;89:4–11.

Waddington H, Aloe AM, Becker BJ, Djimeu EW, Hombrados JG, Tugwell P, et al. Quasi-experimental study designs series—paper 6: risk of bias assessment. J Clin Epidemiol. 2017;89:43–52.

Saeed S, Moodie EEM, Strumpf EC, Klein MB. Evaluating the impact of health policies: using a difference-in-differences approach. Int J Public Health. 2019;64:637–42.

Dunning T. Improving causal inference: strengths and limitations of natural experiments. Polit Res Q. 2008;61:282–93.

Bärnighausen T, Tugwell P, Røttingen JA, Shemilt I, Rockers P, Geldsetzer P, et al. Quasi-experimental study designs series—paper 4: uses and value. J Clin Epidemiol. 2017;89:21–9.

Craig P, Katikireddi SV, Leyland A, Popham F. Natural experiments: an overview of methods, approaches, and contributions to public health intervention research. Annu Rev Public Health. 2017;38:39–56.

Pearl J, Mackenzie D. The book of why: the new science of cause and effect. London: Allen Lane; 2018.

Rosenbaum PR. How to see more in observational studies: some new quasi-experimental devices. Annu Rev Stat Its Appl. 2015;2:21–48.

Petimar J, Ramirez M, Rifas-Shiman SL, Linakis S, Mullen J, Roberto CA, et al. Evaluation of the impact of calorie labeling on McDonald’s restaurant menus: a natural experiment. Int J Behav Nutr Phys Act. 2019;16. Article no: 99.

Fergusson DM, Horwood LJ, Boden JM, Mulder RT. Impact of a major disaster on the mental health of a well-studied cohort. JAMA Psychiatry. 2014;71:1025–31.

Remler DK, Van Ryzin GG. Natural and quasi experiments. In: Research methods in practice: strategies for description and causation. 2nd ed. Thousand Oaks: SAGE Publication Inc.; 2014. p. 467–500.

Cook PA, Hargreaves SC, Burns EJ, De Vocht F, Parrott S, Coffey M, et al. Communities in charge of alcohol (CICA): a protocol for a stepped-wedge randomised control trial of an alcohol health champions programme. BMC Public Health. 2018;18. Article no: 522.

Lumey LH, Stein AD, Kahn HS, Van der Pal-de Bruin KM, Blauw GJ, Zybert PA, et al. Cohort profile: the Dutch hunger winter families study. Int J Epidemiol. 2007;36:1196–204.

Article   CAS   Google Scholar  

Meng X, Qian N. The Long Term Consequences of Famine on Survivors: Evidence from a Unique Natural Experiment using China’s Great Famine. Natl Bur Econ Res Work Pap Ser. 2011;NBER Worki.

Franco M, Bilal U, Orduñez P, Benet M, Morejón A, Caballero B, et al. Population-wide weight loss and regain in relation to diabetes burden and cardiovascular mortality in Cuba 1980-2010: repeated cross sectional surveys and ecological comparison of secular trends. BMJ. 2013;346:f1515.

Angrist J, Bettinger E, Bloom E, King E, Kremer M. Vouchers for private schooling in Colombia: evidence from a randomized natural experiment. Am Econ Rev. 2002;92:1535–58.

Angrist JD. Lifetime earnings and the Vietnam era draft lottery: evidence from social security administrative records. Am Econ Rev. 1990;80:313–36.

Dawson A, Sim J. The nature and ethics of natural experiments. J Med Ethics. 2015;41:848–53.

Bärnighausen T, Oldenburg C, Tugwell P, Bommer C, Ebert C, Barreto M, et al. Quasi-experimental study designs series—paper 7: assessing the assumptions. J Clin Epidemiol. 2017;89:53-66.

Tugwell P, Knottnerus JA, McGowan J, Tricco A. Big-5 Quasi-Experimental designs. J Clin Epidemiol. 2017;89:1–3.

Reeves BC, Wells GA, Waddington H. Quasi-experimental study designs series—paper 5: a checklist for classifying studies evaluating the effects on health interventions—a taxonomy without labels. J Clin Epidemiol. 2017;89:30–42.

Rubin DB. For objective causal inference, design trumps analysis. Ann Appl Stat. 2008;2:808–40.

Hernán MA, Robins JM. Using big data to emulate a target trial when a randomized trial is not available. Am J Epidemiol. 2016;183:758–64.

Benjamin-Chung J, Arnold BF, Berger D, Luby SP, Miguel E, Colford JM, et al. Spillover effects in epidemiology: parameters, study designs and methodological considerations. Int J Epidemiol. 2018;47:332–47.

Munafò MR, Tilling K, Taylor AE, Evans DM, Smith GD. Collider scope: when selection bias can substantially influence observed associations. Int J Epidemiol. 2018;47:226–35.

Schwartz S, Gatto NM, Campbell UB. Extending the sufficient component cause model to describe the stable unit treatment value assumption (SUTVA). Epidemiol Perspect Innov. 2012;9:3.

Cawley J, Thow AM, Wen K, Frisvold D. The economics of taxes on sugar-sweetened beverages: a review of the effects on prices, sales, cross-border shopping, and consumption. Annu Rev Nutr. 2019;39:317–38.

Reichardt CS. Nonequivalent Group Designs. In: Quasi-Experimentation. A Guide to Design and Analysis. 1st edition. New York: The Guildford Press; 2019. p. 112–162.

Denzin N. Sociological methods: a sourcebook. 5th ed. New York: Routledges; 2006.

Matthay EC, Hagan E, Gottlieb LM, Tan ML, Vlahov D, Adler NE, et al. Alternative causal inference methods in population health research: evaluating tradeoffs and triangulating evidence. SSM - Popul Heal. 2020;10:10052.

Leatherdale ST. Natural experiment methodology for research: a review of how different methods can support real-world research. Int J Soc Res Methodol. 2019;22:19–35.

Reichardt CS. Quasi-experimentation. A guide to design and analysis. 1st ed. New York: The Guildford Press; 2019.

Reeves A, McKee M, Mackenbach J, Whitehead M, Stuckler D. Introduction of a National Minimum Wage Reduced Depressive Symptoms in Low-Wage Workers: A Quasi-Natural Experiment in the UK. Heal Econ (United Kingdom). 2017;26:639–55.

Sterne JA, Hernán MA, Reeves BC, Savović J, Berkman ND, Viswanathan M, et al. ROBINS-I: a tool for assessing risk of bias in non-randomised studies of interventions. BMJ. 2016;355:i4919.

Shadish WR, Cook TD, Campbell DT. Generalized Causal Inference: A Grounded Theory. In: Experimental and Quasi-Experimental Designs for Generalized Causal Inference. 2nd ed. Belmont: Wadsworth, Cengage Learning; 2002. p. 341–73.

Lawlor DA, Tilling K, Smith GD. Triangulation in aetiological epidemiology. Int J Epidemiol. 2016;45:1866–86.

Hernán MA. The C-word: scientific euphemisms do not improve causal inference from observational data. Am J Public Health. 2018;108:616–9.

Guyatt G, Oxman AD, Akl EA, Kunz R, Vist G, Brozek J, et al. GRADE guidelines: 1. Introduction - GRADE evidence profiles and summary of findings tables. J Clin Epidemiol. 2011;64:383–94.

Schünemann HJ, Cuello C, Akl EA, Mustafa RA, Meerpohl JJ, Thayer K, et al. GRADE guidelines: 18. How ROBINS-I and other tools to assess risk of bias in nonrandomized studies should be used to rate the certainty of a body of evidence. J Clin Epidemiol. 2019;111:105–14.

Campbell M, Katikireddi SV, Hoffmann T, Armstrong R, Waters E, Craig P. TIDieR-PHP: a reporting guideline for population health and policy interventions. BMJ. 2018;361:k1079.

Mamluk L, Jones T, Ijaz S, Edwards HB, Savović J, Leach V, et al. Evidence of detrimental effects of prenatal alcohol exposure on offspring birthweight and neurodevelopment from a systematic review of quasi-experimental studies. Int J Epidemiol. 2021;49(6):1972-95.

Ogilvie D, Adams J, Bauman A, Gregg EW, Panter J, Siegel KR, et al. Using natural experimental studies to guide public health action: turning the evidence-based medicine paradigm on its head. J Epidemiol Community Health. 2019;74:203–8.

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Acknowledgements

This study is funded by the National Institute for Health Research (NIHR) School for Public Health Research (Grant Reference Number PD-SPH-2015). The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care. The funder had no input in the writing of the manuscript or decision to submit for publication. The NIHR School for Public Health Research is a partnership between the Universities of Sheffield; Bristol; Cambridge; Imperial; and University College London; The London School for Hygiene and Tropical Medicine (LSHTM); LiLaC – a collaboration between the Universities of Liverpool and Lancaster; and Fuse - The Centre for Translational Research in Public Health a collaboration between Newcastle, Durham, Northumbria, Sunderland and Teesside Universities. FdV is partly funded by National Institute for Health Research Applied Research Collaboration West (NIHR ARC West) at University Hospitals Bristol NHS Foundation Trust. SVK and PC acknowledge funding from the Medical Research Council (MC_UU_12017/13) and Scottish Government Chief Scientist Office (SPHSU13). SVK acknowledges funding from a NRS Senior Clinical Fellowship (SCAF/15/02). KT works in the MRC Integrative Epidemiology Unit, which is supported by the Medical Research Council (MRC) and the University of Bristol [MC_UU_00011/3].

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FdV conceived of the study. FdV, SVK,CMQ,KT,MH, PC interpretated the evidence and theory. FdV wrote the first version of the manuscript. SVK,CMQ,KT,MH, PC provided substantive revisions to subsequent versions. All authors have read and approved the manuscript. FdV, SVK,CMQ,KT,MH, PC agreed to be personally accountable for their own contributions and will ensure that questions related to the accuracy or integrity of any part of the work, even ones in which the author was not personally involved, are appropriately investigated, resolved, and the resolution documented in the literature.

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Online Supplementary Material. Table 1 . the Target Trial for Natural Experiments and Reeves et al. [ 28 ]. Alignment of Reeves et al. (Introduction of a National Minimum Wage Reduced Depressive Symptoms in Low-Wage Workers: A Quasi-Natural Experiment in the UK. Heal Econ. 2017;26:639–55) to the Target Trial framework.

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de Vocht, F., Katikireddi, S.V., McQuire, C. et al. Conceptualising natural and quasi experiments in public health. BMC Med Res Methodol 21 , 32 (2021). https://doi.org/10.1186/s12874-021-01224-x

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The use and interpretation of quasi-experimental design

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• What is a quasi-experimental design?

Commonly used in medical informatics (a field that uses digital information to ensure better patient care), researchers generally use this design to evaluate the effectiveness of a treatment – perhaps a type of antibiotic or psychotherapy, or an educational or policy intervention.

Even though quasi-experimental design has been used for some time, relatively little is known about it. Read on to learn the ins and outs of this research design.

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Dovetail streamlines research to help you uncover and share actionable insights

• When to use a quasi-experimental design

A quasi-experimental design is used when it's not logistically feasible or ethical to conduct randomized, controlled trials. As its name suggests, a quasi-experimental design is almost a true experiment. However, researchers don't randomly select elements or participants in this type of research.

Researchers prefer to apply quasi-experimental design when there are ethical or practical concerns. Let's look at these two reasons more closely.

Ethical reasons

In some situations, the use of randomly assigned elements can be unethical. For instance, providing public healthcare to one group and withholding it to another in research is unethical. A quasi-experimental design would examine the relationship between these two groups to avoid physical danger.

Practical reasons

Randomized controlled trials may not be the best approach in research. For instance, it's impractical to trawl through large sample sizes of participants without using a particular attribute to guide your data collection .

Recruiting participants and properly designing a data-collection attribute to make the research a true experiment requires a lot of time and effort, and can be expensive if you don’t have a large funding stream.

A quasi-experimental design allows researchers to take advantage of previously collected data and use it in their study.

• Examples of quasi-experimental designs

Quasi-experimental research design is common in medical research, but any researcher can use it for research that raises practical and ethical concerns. Here are a few examples of quasi-experimental designs used by different researchers:

Example 1: Determining the effectiveness of math apps in supplementing math classes

A school wanted to supplement its math classes with a math app. To select the best app, the school decided to conduct demo tests on two apps before selecting the one they will purchase.

Scope of the research

Since every grade had two math teachers, each teacher used one of the two apps for three months. They then gave the students the same math exams and compared the results to determine which app was most effective.

Reasons why this is a quasi-experimental study

This simple study is a quasi-experiment since the school didn't randomly assign its students to the applications. They used a pre-existing class structure to conduct the study since it was impractical to randomly assign the students to each app.

Example 2: Determining the effectiveness of teaching modern leadership techniques in start-up businesses

A hypothetical quasi-experimental study was conducted in an economically developing country in a mid-sized city.

Five start-ups in the textile industry and five in the tech industry participated in the study. The leaders attended a six-week workshop on leadership style, team management, and employee motivation.

After a year, the researchers assessed the performance of each start-up company to determine growth. The results indicated that the tech start-ups were further along in their growth than the textile companies.

The basis of quasi-experimental research is a non-randomized subject-selection process. This study didn't use specific aspects to determine which start-up companies should participate. Therefore, the results may seem straightforward, but several aspects may determine the growth of a specific company, apart from the variables used by the researchers.

Example 3: A study to determine the effects of policy reforms and of luring foreign investment on small businesses in two mid-size cities

In a study to determine the economic impact of government reforms in an economically developing country, the government decided to test whether creating reforms directed at small businesses or luring foreign investments would spur the most economic development.

The government selected two cities with similar population demographics and sizes. In one of the cities, they implemented specific policies that would directly impact small businesses, and in the other, they implemented policies to attract foreign investment.

After five years, they collected end-of-year economic growth data from both cities. They looked at elements like local GDP growth, unemployment rates, and housing sales.

The study used a non-randomized selection process to determine which city would participate in the research. Researchers left out certain variables that would play a crucial role in determining the growth of each city. They used pre-existing groups of people based on research conducted in each city, rather than random groups.

• Advantages of a quasi-experimental design

Some advantages of quasi-experimental designs are:

Researchers can manipulate variables to help them meet their study objectives.

It offers high external validity, making it suitable for real-world applications, specifically in social science experiments.

Integrating this methodology into other research designs is easier, especially in true experimental research. This cuts down on the time needed to determine your outcomes.

• Disadvantages of a quasi-experimental design

Despite the pros that come with a quasi-experimental design, there are several disadvantages associated with it, including the following:

It has a lower internal validity since researchers do not have full control over the comparison and intervention groups or between time periods because of differences in characteristics in people, places, or time involved. It may be challenging to determine whether all variables have been used or whether those used in the research impacted the results.

There is the risk of inaccurate data since the research design borrows information from other studies.

There is the possibility of bias since researchers select baseline elements and eligibility.

• What are the different quasi-experimental study designs?

There are three distinct types of quasi-experimental designs:

Nonequivalent

Regression discontinuity, natural experiment.

This is a hybrid of experimental and quasi-experimental methods and is used to leverage the best qualities of the two. Like the true experiment design, nonequivalent group design uses pre-existing groups believed to be comparable. However, it doesn't use randomization, the lack of which is a crucial element for quasi-experimental design.

Researchers usually ensure that no confounding variables impact them throughout the grouping process. This makes the groupings more comparable.

Example of a nonequivalent group design

A small study was conducted to determine whether after-school programs result in better grades. Researchers randomly selected two groups of students: one to implement the new program, the other not to. They then compared the results of the two groups.

This type of quasi-experimental research design calculates the impact of a specific treatment or intervention. It uses a criterion known as "cutoff" that assigns treatment according to eligibility.

Researchers often assign participants above the cutoff to the treatment group. This puts a negligible distinction between the two groups (treatment group and control group).

Example of regression discontinuity

Students must achieve a minimum score to be enrolled in specific US high schools. Since the cutoff score used to determine eligibility for enrollment is arbitrary, researchers can assume that the disparity between students who only just fail to achieve the cutoff point and those who barely pass is a small margin and is due to the difference in the schools that these students attend.

Researchers can then examine the long-term effects of these two groups of kids to determine the effect of attending certain schools. This information can be applied to increase the chances of students being enrolled in these high schools.

This research design is common in laboratory and field experiments where researchers control target subjects by assigning them to different groups. Researchers randomly assign subjects to a treatment group using nature or an external event or situation.

However, even with random assignment, this research design cannot be called a true experiment since nature aspects are observational. Researchers can also exploit these aspects despite having no control over the independent variables.

Example of the natural experiment approach

An example of a natural experiment is the 2008 Oregon Health Study.

Oregon intended to allow more low-income people to participate in Medicaid.

Since they couldn't afford to cover every person who qualified for the program, the state used a random lottery to allocate program slots.

Researchers assessed the program's effectiveness by assigning the selected subjects to a randomly assigned treatment group, while those that didn't win the lottery were considered the control group.

• Differences between quasi-experiments and true experiments

There are several differences between a quasi-experiment and a true experiment:

Participants in true experiments are randomly assigned to the treatment or control group, while participants in a quasi-experiment are not assigned randomly.

In a quasi-experimental design, the control and treatment groups differ in unknown or unknowable ways, apart from the experimental treatments that are carried out. Therefore, the researcher should try as much as possible to control these differences.

Quasi-experimental designs have several "competing hypotheses," which compete with experimental manipulation to explain the observed results.

Quasi-experiments tend to have lower internal validity (the degree of confidence in the research outcomes) than true experiments, but they may offer higher external validity (whether findings can be extended to other contexts) as they involve real-world interventions instead of controlled interventions in artificial laboratory settings.

Despite the distinct difference between true and quasi-experimental research designs, these two research methodologies share the following aspects:

Both study methods subject participants to some form of treatment or conditions.

Researchers have the freedom to measure some of the outcomes of interest.

Researchers can test whether the differences in the outcomes are associated with the treatment.

• An example comparing a true experiment and quasi-experiment

Imagine you wanted to study the effects of junk food on obese people. Here's how you would do this as a true experiment and a quasi-experiment:

How to carry out a true experiment

In a true experiment, some participants would eat junk foods, while the rest would be in the control group, adhering to a regular diet. At the end of the study, you would record the health and discomfort of each group.

This kind of experiment would raise ethical concerns since the participants assigned to the treatment group are required to eat junk food against their will throughout the experiment. This calls for a quasi-experimental design.

How to carry out a quasi-experiment

In quasi-experimental research, you would start by finding out which participants want to try junk food and which prefer to stick to a regular diet. This allows you to assign these two groups based on subject choice.

In this case, you didn't assign participants to a particular group, so you can confidently use the results from the study.

When is a quasi-experimental design used?

Quasi-experimental designs are used when researchers don’t want to use randomization when evaluating their intervention.

What are the characteristics of quasi-experimental designs?

Some of the characteristics of a quasi-experimental design are:

Researchers don't randomly assign participants into groups, but study their existing characteristics and assign them accordingly.

Researchers study the participants in pre- and post-testing to determine the progress of the groups.

Quasi-experimental design is ethical since it doesn’t involve offering or withholding treatment at random.

Quasi-experimental design encompasses a broad range of non-randomized intervention studies. This design is employed when it is not ethical or logistically feasible to conduct randomized controlled trials. Researchers typically employ it when evaluating policy or educational interventions, or in medical or therapy scenarios.

How do you analyze data in a quasi-experimental design?

You can use two-group tests, time-series analysis, and regression analysis to analyze data in a quasi-experiment design. Each option has specific assumptions, strengths, limitations, and data requirements.

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Introduction, validity concerns, time series designs.

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Although the randomized trial is considered the optimal design for testing cause-and-effect hypotheses, the necessary restrictions of a randomized trial are not always possible within the clinical environment. Depending on the nature of the treatment under study and the population of interest, use of randomization and control groups may not be possible.

Quasi-experimental designs utilize similar structures to experimental designs, but lack either random assignment, comparison groups, or both. Even with these limitations, these designs represent an important contribution to clinical research because they accommodate for the limitations of natural settings, where scheduling treatment conditions and random assignment are often difficult, impractical, or unethical. They are often used in pragmatic studies because of the logistic limitations that occur in practice. The purpose of this chapter is to describe time series designs and nonequivalent group designs, the two basic structures of quasi-experimental research.

Because quasi-experimental designs lack at least one of the requirements for controlled trials, they cannot rule out threats to internal validity with the same confidence as experimental studies. Nonequivalent groups may differ from each other in many ways in addition to differences between treatment conditions. Therefore, the degree of control is reduced.

Quasi-experimental designs present reasonable alternatives to the randomized trial as long as the researcher carefully documents subject characteristics, controls the research protocol, and uses blinding as much as possible. The conclusions drawn from these studies must take into account the potential biases of the sample, but may provide important information, nonetheless.

Many research questions focus on the variation of responses over time. In such a design, time becomes an independent variable with several levels and researchers will look for differences across time intervals. Such designs can be configured in several ways, with varying degrees of control.

One-Group Pretest–Posttest Design

The one-group pretest–posttest design is a quasi-experimental design that involves one set of repeated measurements taken before and after treatment on one group of subjects (see Fig. 17-1 ). The effect of treatment is determined by measuring the difference between pretest and posttest scores.

Figure 17–1

A one-group pretest–posttest design. The independent variable is time, with two levels (T1 and T2).

In this design, the independent variable is time, with two levels (pretest and posttest). Treatment is not an independent variable because all subjects receive the intervention.

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Experimental and quasi-experimental designs in implementation research

Affiliations.

• 1 VA Boston Healthcare System, Center for Healthcare Organization and Implementation Research (CHOIR), United States Department of Veterans Affairs, Boston, MA, USA; Department of Psychiatry, Harvard Medical School, Boston, MA, USA. Electronic address: [email protected].
• 2 Department of Psychiatry, University of Michigan Medical School, Ann Arbor, MI, USA; Survey Research Center, Institute for Social Research, University of Michigan, Ann Arbor, MI, USA.
• 3 VA Boston Healthcare System, Center for Healthcare Organization and Implementation Research (CHOIR), United States Department of Veterans Affairs, Boston, MA, USA.
• PMID: 31255320
• PMCID: PMC6923620
• DOI: 10.1016/j.psychres.2019.06.027

Implementation science is focused on maximizing the adoption, appropriate use, and sustainability of effective clinical practices in real world clinical settings. Many implementation science questions can be feasibly answered by fully experimental designs, typically in the form of randomized controlled trials (RCTs). Implementation-focused RCTs, however, usually differ from traditional efficacy- or effectiveness-oriented RCTs on key parameters. Other implementation science questions are more suited to quasi-experimental designs, which are intended to estimate the effect of an intervention in the absence of randomization. These designs include pre-post designs with a non-equivalent control group, interrupted time series (ITS), and stepped wedges, the last of which require all participants to receive the intervention, but in a staggered fashion. In this article we review the use of experimental designs in implementation science, including recent methodological advances for implementation studies. We also review the use of quasi-experimental designs in implementation science, and discuss the strengths and weaknesses of these approaches. This article is therefore meant to be a practical guide for researchers who are interested in selecting the most appropriate study design to answer relevant implementation science questions, and thereby increase the rate at which effective clinical practices are adopted, spread, and sustained.

Keywords: Implementation; Interrupted time series; Pre-post with non-equivalent control group; Quasi-experimental; SMART design; Stepped wedge.

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Home » Quasi-Experimental Research Design – Types, Methods

Quasi-Experimental Research Design – Types, Methods

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Quasi-Experimental Design

Quasi-experimental design is a research method that seeks to evaluate the causal relationships between variables, but without the full control over the independent variable(s) that is available in a true experimental design.

In a quasi-experimental design, the researcher uses an existing group of participants that is not randomly assigned to the experimental and control groups. Instead, the groups are selected based on pre-existing characteristics or conditions, such as age, gender, or the presence of a certain medical condition.

Types of Quasi-Experimental Design

There are several types of quasi-experimental designs that researchers use to study causal relationships between variables. Here are some of the most common types:

Non-Equivalent Control Group Design

This design involves selecting two groups of participants that are similar in every way except for the independent variable(s) that the researcher is testing. One group receives the treatment or intervention being studied, while the other group does not. The two groups are then compared to see if there are any significant differences in the outcomes.

Interrupted Time-Series Design

This design involves collecting data on the dependent variable(s) over a period of time, both before and after an intervention or event. The researcher can then determine whether there was a significant change in the dependent variable(s) following the intervention or event.

Pretest-Posttest Design

This design involves measuring the dependent variable(s) before and after an intervention or event, but without a control group. This design can be useful for determining whether the intervention or event had an effect, but it does not allow for control over other factors that may have influenced the outcomes.

Regression Discontinuity Design

This design involves selecting participants based on a specific cutoff point on a continuous variable, such as a test score. Participants on either side of the cutoff point are then compared to determine whether the intervention or event had an effect.

Natural Experiments

This design involves studying the effects of an intervention or event that occurs naturally, without the researcher’s intervention. For example, a researcher might study the effects of a new law or policy that affects certain groups of people. This design is useful when true experiments are not feasible or ethical.

Data Analysis Methods

Here are some data analysis methods that are commonly used in quasi-experimental designs:

Descriptive Statistics

This method involves summarizing the data collected during a study using measures such as mean, median, mode, range, and standard deviation. Descriptive statistics can help researchers identify trends or patterns in the data, and can also be useful for identifying outliers or anomalies.

Inferential Statistics

This method involves using statistical tests to determine whether the results of a study are statistically significant. Inferential statistics can help researchers make generalizations about a population based on the sample data collected during the study. Common statistical tests used in quasi-experimental designs include t-tests, ANOVA, and regression analysis.

Propensity Score Matching

This method is used to reduce bias in quasi-experimental designs by matching participants in the intervention group with participants in the control group who have similar characteristics. This can help to reduce the impact of confounding variables that may affect the study’s results.

Difference-in-differences Analysis

This method is used to compare the difference in outcomes between two groups over time. Researchers can use this method to determine whether a particular intervention has had an impact on the target population over time.

Interrupted Time Series Analysis

This method is used to examine the impact of an intervention or treatment over time by comparing data collected before and after the intervention or treatment. This method can help researchers determine whether an intervention had a significant impact on the target population.

Regression Discontinuity Analysis

This method is used to compare the outcomes of participants who fall on either side of a predetermined cutoff point. This method can help researchers determine whether an intervention had a significant impact on the target population.

Steps in Quasi-Experimental Design

Here are the general steps involved in conducting a quasi-experimental design:

• Identify the research question: Determine the research question and the variables that will be investigated.
• Choose the design: Choose the appropriate quasi-experimental design to address the research question. Examples include the pretest-posttest design, non-equivalent control group design, regression discontinuity design, and interrupted time series design.
• Select the participants: Select the participants who will be included in the study. Participants should be selected based on specific criteria relevant to the research question.
• Measure the variables: Measure the variables that are relevant to the research question. This may involve using surveys, questionnaires, tests, or other measures.
• Implement the intervention or treatment: Implement the intervention or treatment to the participants in the intervention group. This may involve training, education, counseling, or other interventions.
• Collect data: Collect data on the dependent variable(s) before and after the intervention. Data collection may also include collecting data on other variables that may impact the dependent variable(s).
• Analyze the data: Analyze the data collected to determine whether the intervention had a significant impact on the dependent variable(s).
• Draw conclusions: Draw conclusions about the relationship between the independent and dependent variables. If the results suggest a causal relationship, then appropriate recommendations may be made based on the findings.

Quasi-Experimental Design Examples

Here are some examples of real-time quasi-experimental designs:

• Evaluating the impact of a new teaching method: In this study, a group of students are taught using a new teaching method, while another group is taught using the traditional method. The test scores of both groups are compared before and after the intervention to determine whether the new teaching method had a significant impact on student performance.
• Assessing the effectiveness of a public health campaign: In this study, a public health campaign is launched to promote healthy eating habits among a targeted population. The behavior of the population is compared before and after the campaign to determine whether the intervention had a significant impact on the target behavior.
• Examining the impact of a new medication: In this study, a group of patients is given a new medication, while another group is given a placebo. The outcomes of both groups are compared to determine whether the new medication had a significant impact on the targeted health condition.
• Evaluating the effectiveness of a job training program : In this study, a group of unemployed individuals is enrolled in a job training program, while another group is not enrolled in any program. The employment rates of both groups are compared before and after the intervention to determine whether the training program had a significant impact on the employment rates of the participants.
• Assessing the impact of a new policy : In this study, a new policy is implemented in a particular area, while another area does not have the new policy. The outcomes of both areas are compared before and after the intervention to determine whether the new policy had a significant impact on the targeted behavior or outcome.

Applications of Quasi-Experimental Design

Here are some applications of quasi-experimental design:

• Educational research: Quasi-experimental designs are used to evaluate the effectiveness of educational interventions, such as new teaching methods, technology-based learning, or educational policies.
• Health research: Quasi-experimental designs are used to evaluate the effectiveness of health interventions, such as new medications, public health campaigns, or health policies.
• Social science research: Quasi-experimental designs are used to investigate the impact of social interventions, such as job training programs, welfare policies, or criminal justice programs.
• Business research: Quasi-experimental designs are used to evaluate the impact of business interventions, such as marketing campaigns, new products, or pricing strategies.
• Environmental research: Quasi-experimental designs are used to evaluate the impact of environmental interventions, such as conservation programs, pollution control policies, or renewable energy initiatives.

When to use Quasi-Experimental Design

Here are some situations where quasi-experimental designs may be appropriate:

• When the research question involves investigating the effectiveness of an intervention, policy, or program : In situations where it is not feasible or ethical to randomly assign participants to intervention and control groups, quasi-experimental designs can be used to evaluate the impact of the intervention on the targeted outcome.
• When the sample size is small: In situations where the sample size is small, it may be difficult to randomly assign participants to intervention and control groups. Quasi-experimental designs can be used to investigate the impact of an intervention without requiring a large sample size.
• When the research question involves investigating a naturally occurring event : In some situations, researchers may be interested in investigating the impact of a naturally occurring event, such as a natural disaster or a major policy change. Quasi-experimental designs can be used to evaluate the impact of the event on the targeted outcome.
• When the research question involves investigating a long-term intervention: In situations where the intervention or program is long-term, it may be difficult to randomly assign participants to intervention and control groups for the entire duration of the intervention. Quasi-experimental designs can be used to evaluate the impact of the intervention over time.
• When the research question involves investigating the impact of a variable that cannot be manipulated : In some situations, it may not be possible or ethical to manipulate a variable of interest. Quasi-experimental designs can be used to investigate the relationship between the variable and the targeted outcome.

Purpose of Quasi-Experimental Design

The purpose of quasi-experimental design is to investigate the causal relationship between two or more variables when it is not feasible or ethical to conduct a randomized controlled trial (RCT). Quasi-experimental designs attempt to emulate the randomized control trial by mimicking the control group and the intervention group as much as possible.

The key purpose of quasi-experimental design is to evaluate the impact of an intervention, policy, or program on a targeted outcome while controlling for potential confounding factors that may affect the outcome. Quasi-experimental designs aim to answer questions such as: Did the intervention cause the change in the outcome? Would the outcome have changed without the intervention? And was the intervention effective in achieving its intended goals?

Quasi-experimental designs are useful in situations where randomized controlled trials are not feasible or ethical. They provide researchers with an alternative method to evaluate the effectiveness of interventions, policies, and programs in real-life settings. Quasi-experimental designs can also help inform policy and practice by providing valuable insights into the causal relationships between variables.

Overall, the purpose of quasi-experimental design is to provide a rigorous method for evaluating the impact of interventions, policies, and programs while controlling for potential confounding factors that may affect the outcome.

Advantages of Quasi-Experimental Design

Quasi-experimental designs have several advantages over other research designs, such as:

• Greater external validity : Quasi-experimental designs are more likely to have greater external validity than laboratory experiments because they are conducted in naturalistic settings. This means that the results are more likely to generalize to real-world situations.
• Ethical considerations: Quasi-experimental designs often involve naturally occurring events, such as natural disasters or policy changes. This means that researchers do not need to manipulate variables, which can raise ethical concerns.
• More practical: Quasi-experimental designs are often more practical than experimental designs because they are less expensive and easier to conduct. They can also be used to evaluate programs or policies that have already been implemented, which can save time and resources.
• No random assignment: Quasi-experimental designs do not require random assignment, which can be difficult or impossible in some cases, such as when studying the effects of a natural disaster. This means that researchers can still make causal inferences, although they must use statistical techniques to control for potential confounding variables.
• Greater generalizability : Quasi-experimental designs are often more generalizable than experimental designs because they include a wider range of participants and conditions. This can make the results more applicable to different populations and settings.

Limitations of Quasi-Experimental Design

There are several limitations associated with quasi-experimental designs, which include:

• Lack of Randomization: Quasi-experimental designs do not involve randomization of participants into groups, which means that the groups being studied may differ in important ways that could affect the outcome of the study. This can lead to problems with internal validity and limit the ability to make causal inferences.
• Selection Bias: Quasi-experimental designs may suffer from selection bias because participants are not randomly assigned to groups. Participants may self-select into groups or be assigned based on pre-existing characteristics, which may introduce bias into the study.
• History and Maturation: Quasi-experimental designs are susceptible to history and maturation effects, where the passage of time or other events may influence the outcome of the study.
• Lack of Control: Quasi-experimental designs may lack control over extraneous variables that could influence the outcome of the study. This can limit the ability to draw causal inferences from the study.
• Limited Generalizability: Quasi-experimental designs may have limited generalizability because the results may only apply to the specific population and context being studied.

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The Use and Interpretation of Quasi-Experimental Studies in Medical Informatics

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Anthony D. Harris, Jessina C. McGregor, Eli N. Perencevich, Jon P. Furuno, Jingkun Zhu, Dan E. Peterson, Joseph Finkelstein, The Use and Interpretation of Quasi-Experimental Studies in Medical Informatics, Journal of the American Medical Informatics Association , Volume 13, Issue 1, January 2006, Pages 16–23, https://doi.org/10.1197/jamia.M1749

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Quasi-experimental study designs, often described as nonrandomized, pre-post intervention studies, are common in the medical informatics literature. Yet little has been written about the benefits and limitations of the quasi-experimental approach as applied to informatics studies. This paper outlines a relative hierarchy and nomenclature of quasi-experimental study designs that is applicable to medical informatics intervention studies. In addition, the authors performed a systematic review of two medical informatics journals, the Journal of the American Medical Informatics Association (JAMIA) and the International Journal of Medical Informatics (IJMI), to determine the number of quasi-experimental studies published and how the studies are classified on the above-mentioned relative hierarchy. They hope that future medical informatics studies will implement higher level quasi-experimental study designs that yield more convincing evidence for causal links between medical informatics interventions and outcomes.

Quasi-experimental studies encompass a broad range of nonrandomized intervention studies. These designs are frequently used when it is not logistically feasible or ethical to conduct a randomized controlled trial. Examples of quasi-experimental studies follow. As one example of a quasi-experimental study, a hospital introduces a new order-entry system and wishes to study the impact of this intervention on the number of medication-related adverse events before and after the intervention. As another example, an informatics technology group is introducing a pharmacy order-entry system aimed at decreasing pharmacy costs. The intervention is implemented and pharmacy costs before and after the intervention are measured.

In medical informatics, the quasi-experimental, sometimes called the pre-post intervention, design often is used to evaluate the benefits of specific interventions. The increasing capacity of health care institutions to collect routine clinical data has led to the growing use of quasi-experimental study designs in the field of medical informatics as well as in other medical disciplines. However, little is written about these study designs in the medical literature or in traditional epidemiology textbooks. 1–3 In contrast, the social sciences literature is replete with examples of ways to implement and improve quasi-experimental studies. 4–6

In this paper, we review the different pretest-posttest quasi-experimental study designs, their nomenclature, and the relative hierarchy of these designs with respect to their ability to establish causal associations between an intervention and an outcome. The example of a pharmacy order-entry system aimed at decreasing pharmacy costs will be used throughout this article to illustrate the different quasi-experimental designs. We discuss limitations of quasi-experimental designs and offer methods to improve them. We also perform a systematic review of four years of publications from two informatics journals to determine the number of quasi-experimental studies, classify these studies into their application domains, determine whether the potential limitations of quasi-experimental studies were acknowledged by the authors, and place these studies into the above-mentioned relative hierarchy.

The authors reviewed articles and book chapters on the design of quasi-experimental studies. 4–10 Most of the reviewed articles referenced two textbooks that were then reviewed in depth. 4 , 6

Key advantages and disadvantages of quasi-experimental studies, as they pertain to the study of medical informatics, were identified. The potential methodological flaws of quasi-experimental medical informatics studies, which have the potential to introduce bias, were also identified. In addition, a summary table outlining a relative hierarchy and nomenclature of quasi-experimental study designs is described. In general, the higher the design is in the hierarchy, the greater the internal validity that the study traditionally possesses because the evidence of the potential causation between the intervention and the outcome is strengthened. 4

We then performed a systematic review of four years of publications from two informatics journals. First, we determined the number of quasi-experimental studies. We then classified these studies on the above-mentioned hierarchy. We also classified the quasi-experimental studies according to their application domain. The categories of application domains employed were based on categorization used by Yearbooks of Medical Informatics 1992–2005 and were similar to the categories of application domains employed by Annual Symposiums of the American Medical Informatics Association. 11 The categories were (1) health and clinical management; (2) patient records; (3) health information systems; (4) medical signal processing and biomedical imaging; (5) decision support, knowledge representation, and management; (6) education and consumer informatics; and (7) bioinformatics. Because the quasi-experimental study design has recognized limitations, we sought to determine whether authors acknowledged the potential limitations of this design. Examples of acknowledgment included mention of lack of randomization, the potential for regression to the mean, the presence of temporal confounders and the mention of another design that would have more internal validity.

All original scientific manuscripts published between January 2000 and December 2003 in the Journal of the American Medical Informatics Association (JAMIA) and the International Journal of Medical Informatics (IJMI) were reviewed. One author (ADH) reviewed all the papers to identify the number of quasi-experimental studies. Other authors (ADH, JCM, JF) then independently reviewed all the studies identified as quasi-experimental. The three authors then convened as a group to resolve any disagreements in study classification, application domain, and acknowledgment of limitations.

What Is a Quasi-experiment?

Quasi-experiments are studies that aim to evaluate interventions but that do not use randomization. Similar to randomized trials, quasi-experiments aim to demonstrate causality between an intervention and an outcome. Quasi-experimental studies can use both preintervention and postintervention measurements as well as nonrandomly selected control groups.

Using this basic definition, it is evident that many published studies in medical informatics utilize the quasi-experimental design. Although the randomized controlled trial is generally considered to have the highest level of credibility with regard to assessing causality, in medical informatics, researchers often choose not to randomize the intervention for one or more reasons: (1) ethical considerations, (2) difficulty of randomizing subjects, (3) difficulty to randomize by locations (e.g., by wards), (4) small available sample size. Each of these reasons is discussed below.

Ethical considerations typically will not allow random withholding of an intervention with known efficacy. Thus, if the efficacy of an intervention has not been established, a randomized controlled trial is the design of choice to determine efficacy. But if the intervention under study incorporates an accepted, well-established therapeutic intervention, or if the intervention has either questionable efficacy or safety based on previously conducted studies, then the ethical issues of randomizing patients are sometimes raised. In the area of medical informatics, it is often believed prior to an implementation that an informatics intervention will likely be beneficial and thus medical informaticians and hospital administrators are often reluctant to randomize medical informatics interventions. In addition, there is often pressure to implement the intervention quickly because of its believed efficacy, thus not allowing researchers sufficient time to plan a randomized trial.

For medical informatics interventions, it is often difficult to randomize the intervention to individual patients or to individual informatics users. So while this randomization is technically possible, it is underused and thus compromises the eventual strength of concluding that an informatics intervention resulted in an outcome. For example, randomly allowing only half of medical residents to use pharmacy order-entry software at a tertiary care hospital is a scenario that hospital administrators and informatics users may not agree to for numerous reasons.

Similarly, informatics interventions often cannot be randomized to individual locations. Using the pharmacy order-entry system example, it may be difficult to randomize use of the system to only certain locations in a hospital or portions of certain locations. For example, if the pharmacy order-entry system involves an educational component, then people may apply the knowledge learned to nonintervention wards, thereby potentially masking the true effect of the intervention. When a design using randomized locations is employed successfully, the locations may be different in other respects (confounding variables), and this further complicates the analysis and interpretation.

In situations where it is known that only a small sample size will be available to test the efficacy of an intervention, randomization may not be a viable option. Randomization is beneficial because on average it tends to evenly distribute both known and unknown confounding variables between the intervention and control group. However, when the sample size is small, randomization may not adequately accomplish this balance. Thus, alternative design and analytical methods are often used in place of randomization when only small sample sizes are available.

What Are the Threats to Establishing Causality When Using Quasi-experimental Designs in Medical Informatics?

The lack of random assignment is the major weakness of the quasi-experimental study design. Associations identified in quasi-experiments meet one important requirement of causality since the intervention precedes the measurement of the outcome. Another requirement is that the outcome can be demonstrated to vary statistically with the intervention. Unfortunately, statistical association does not imply causality, especially if the study is poorly designed. Thus, in many quasi-experiments, one is most often left with the question: “Are there alternative explanations for the apparent causal association?” If these alternative explanations are credible, then the evidence of causation is less convincing. These rival hypotheses, or alternative explanations, arise from principles of epidemiologic study design.

Shadish et al. 4 outline nine threats to internal validity that are outlined in Table 1 . Internal validity is defined as the degree to which observed changes in outcomes can be correctly inferred to be caused by an exposure or an intervention. In quasi-experimental studies of medical informatics, we believe that the methodological principles that most often result in alternative explanations for the apparent causal effect include (a) difficulty in measuring or controlling for important confounding variables , particularly unmeasured confounding variables, which can be viewed as a subset of the selection threat in Table 1 ; (b) results being explained by the statistical principle of regression to the mean . Each of these latter two principles is discussed in turn.

Threats to Internal Validity

Adapted from Shadish et al. 4

An inability to sufficiently control for important confounding variables arises from the lack of randomization. A variable is a confounding variable if it is associated with the exposure of interest and is also associated with the outcome of interest; the confounding variable leads to a situation where a causal association between a given exposure and an outcome is observed as a result of the influence of the confounding variable. For example, in a study aiming to demonstrate that the introduction of a pharmacy order-entry system led to lower pharmacy costs, there are a number of important potential confounding variables (e.g., severity of illness of the patients, knowledge and experience of the software users, other changes in hospital policy) that may have differed in the preintervention and postintervention time periods ( Fig. 1 ). In a multivariable regression, the first confounding variable could be addressed with severity of illness measures, but the second confounding variable would be difficult if not nearly impossible to measure and control. In addition, potential confounding variables that are unmeasured or immeasurable cannot be controlled for in nonrandomized quasi-experimental study designs and can only be properly controlled by the randomization process in randomized controlled trials.

Example of confounding. To get the true effect of the intervention of interest, we need to control for the confounding variable.

Another important threat to establishing causality is regression to the mean. 12–14 This widespread statistical phenomenon can result in wrongly concluding that an effect is due to the intervention when in reality it is due to chance. The phenomenon was first described in 1886 by Francis Galton who measured the adult height of children and their parents. He noted that when the average height of the parents was greater than the mean of the population, the children tended to be shorter than their parents, and conversely, when the average height of the parents was shorter than the population mean, the children tended to be taller than their parents.

In medical informatics, what often triggers the development and implementation of an intervention is a rise in the rate above the mean or norm. For example, increasing pharmacy costs and adverse events may prompt hospital informatics personnel to design and implement pharmacy order-entry systems. If this rise in costs or adverse events is really just an extreme observation that is still within the normal range of the hospital's pharmaceutical costs (i.e., the mean pharmaceutical cost for the hospital has not shifted), then the statistical principle of regression to the mean predicts that these elevated rates will tend to decline even without intervention. However, often informatics personnel and hospital administrators cannot wait passively for this decline to occur. Therefore, hospital personnel often implement one or more interventions, and if a decline in the rate occurs, they may mistakenly conclude that the decline is causally related to the intervention. In fact, an alternative explanation for the finding could be regression to the mean.

What Are the Different Quasi-experimental Study Designs?

In the social sciences literature, quasi-experimental studies are divided into four study design groups 4 , 6 :

Quasi-experimental designs without control groups

Quasi-experimental designs that use control groups but no pretest

Quasi-experimental designs that use control groups and pretests

Interrupted time-series designs

There is a relative hierarchy within these categories of study designs, with category D studies being sounder than categories C, B, or A in terms of establishing causality. Thus, if feasible from a design and implementation point of view, investigators should aim to design studies that fall in to the higher rated categories. Shadish et al. 4 discuss 17 possible designs, with seven designs falling into category A, three designs in category B, and six designs in category C, and one major design in category D. In our review, we determined that most medical informatics quasi-experiments could be characterized by 11 of 17 designs, with six study designs in category A, one in category B, three designs in category C, and one design in category D because the other study designs were not used or feasible in the medical informatics literature. Thus, for simplicity, we have summarized the 11 study designs most relevant to medical informatics research in Table 2 .

Relative Hierarchy of Quasi-experimental Designs

O = Observational Measurement; X = Intervention Under Study. Time moves from left to right.

In general, studies in category D are of higher study design quality than studies in category C, which are higher than those in category B, which are higher than those in category A. Also, as one moves down within each category, the studies become of higher quality, e.g., study 5 in category A is of higher study design quality than study 4, etc.

The nomenclature and relative hierarchy were used in the systematic review of four years of JAMIA and the IJMI. Similar to the relative hierarchy that exists in the evidence-based literature that assigns a hierarchy to randomized controlled trials, cohort studies, case-control studies, and case series, the hierarchy in Table 2 is not absolute in that in some cases, it may be infeasible to perform a higher level study. For example, there may be instances where an A6 design established stronger causality than a B1 design. 15–17

Quasi-experimental Designs without Control Groups

The one-group posttest-only design.

Here, X is the intervention and O is the outcome variable (this notation is continued throughout the article). In this study design, an intervention (X) is implemented and a posttest observation (O1) is taken. For example, X could be the introduction of a pharmacy order-entry intervention and O1 could be the pharmacy costs following the intervention. This design is the weakest of the quasi-experimental designs that are discussed in this article. Without any pretest observations or a control group, there are multiple threats to internal validity. Unfortunately, this study design is often used in medical informatics when new software is introduced since it may be difficult to have pretest measurements due to time, technical, or cost constraints.

The One-Group Pretest-Posttest Design

This is a commonly used study design. A single pretest measurement is taken (O1), an intervention (X) is implemented, and a posttest measurement is taken (O2). In this instance, period O1 frequently serves as the “control” period. For example, O1 could be pharmacy costs prior to the intervention, X could be the introduction of a pharmacy order-entry system, and O2 could be the pharmacy costs following the intervention. Including a pretest provides some information about what the pharmacy costs would have been had the intervention not occurred.

The One-Group Pretest-Posttest Design Using a Double Pretest

The advantage of this study design over A2 is that adding a second pretest prior to the intervention helps provide evidence that can be used to refute the phenomenon of regression to the mean and confounding as alternative explanations for any observed association between the intervention and the posttest outcome. For example, in a study where a pharmacy order-entry system led to lower pharmacy costs (O3 < O2 and O1), if one had two preintervention measurements of pharmacy costs (O1 and O2) and they were both elevated, this would suggest that there was a decreased likelihood that O3 is lower due to confounding and regression to the mean. Similarly, extending this study design by increasing the number of measurements postintervention could also help to provide evidence against confounding and regression to the mean as alternate explanations for observed associations.

The One-Group Pretest-Posttest Design Using a Nonequivalent Dependent Variable

This design involves the inclusion of a nonequivalent dependent variable ( b ) in addition to the primary dependent variable ( a ). Variables a and b should assess similar constructs; that is, the two measures should be affected by similar factors and confounding variables except for the effect of the intervention. Variable a is expected to change because of the intervention X, whereas variable b is not. Taking our example, variable a could be pharmacy costs and variable b could be the length of stay of patients. If our informatics intervention is aimed at decreasing pharmacy costs, we would expect to observe a decrease in pharmacy costs but not in the average length of stay of patients. However, a number of important confounding variables, such as severity of illness and knowledge of software users, might affect both outcome measures. Thus, if the average length of stay did not change following the intervention but pharmacy costs did, then the data are more convincing than if just pharmacy costs were measured.

The Removed-Treatment Design

This design adds a third posttest measurement (O3) to the one-group pretest-posttest design and then removes the intervention before a final measure (O4) is made. The advantage of this design is that it allows one to test hypotheses about the outcome in the presence of the intervention and in the absence of the intervention. Thus, if one predicts a decrease in the outcome between O1 and O2 (after implementation of the intervention), then one would predict an increase in the outcome between O3 and O4 (after removal of the intervention). One caveat is that if the intervention is thought to have persistent effects, then O4 needs to be measured after these effects are likely to have disappeared. For example, a study would be more convincing if it demonstrated that pharmacy costs decreased after pharmacy order-entry system introduction (O2 and O3 less than O1) and that when the order-entry system was removed or disabled, the costs increased (O4 greater than O2 and O3 and closer to O1). In addition, there are often ethical issues in this design in terms of removing an intervention that may be providing benefit.

The Repeated-Treatment Design

The advantage of this design is that it demonstrates reproducibility of the association between the intervention and the outcome. For example, the association is more likely to be causal if one demonstrates that a pharmacy order-entry system results in decreased pharmacy costs when it is first introduced and again when it is reintroduced following an interruption of the intervention. As for design A5, the assumption must be made that the effect of the intervention is transient, which is most often applicable to medical informatics interventions. Because in this design, subjects may serve as their own controls, this may yield greater statistical efficiency with fewer numbers of subjects.

Quasi-experimental Designs That Use a Control Group but No Pretest

Posttest-only design with nonequivalent groups:.

An intervention X is implemented for one group and compared to a second group. The use of a comparison group helps prevent certain threats to validity including the ability to statistically adjust for confounding variables. Because in this study design, the two groups may not be equivalent (assignment to the groups is not by randomization), confounding may exist. For example, suppose that a pharmacy order-entry intervention was instituted in the medical intensive care unit (MICU) and not the surgical intensive care unit (SICU). O1 would be pharmacy costs in the MICU after the intervention and O2 would be pharmacy costs in the SICU after the intervention. The absence of a pretest makes it difficult to know whether a change has occurred in the MICU. Also, the absence of pretest measurements comparing the SICU to the MICU makes it difficult to know whether differences in O1 and O2 are due to the intervention or due to other differences in the two units (confounding variables).

Quasi-experimental Designs That Use Control Groups and Pretests

The reader should note that with all the studies in this category, the intervention is not randomized. The control groups chosen are comparison groups. Obtaining pretest measurements on both the intervention and control groups allows one to assess the initial comparability of the groups. The assumption is that if the intervention and the control groups are similar at the pretest, the smaller the likelihood there is of important confounding variables differing between the two groups.

Untreated Control Group with Dependent Pretest and Posttest Samples:

The use of both a pretest and a comparison group makes it easier to avoid certain threats to validity. However, because the two groups are nonequivalent (assignment to the groups is not by randomization), selection bias may exist. Selection bias exists when selection results in differences in unit characteristics between conditions that may be related to outcome differences. For example, suppose that a pharmacy order-entry intervention was instituted in the MICU and not the SICU. If preintervention pharmacy costs in the MICU (O1a) and SICU (O1b) are similar, it suggests that it is less likely that there are differences in the important confounding variables between the two units. If MICU postintervention costs (O2a) are less than preintervention MICU costs (O1a), but SICU costs (O1b) and (O2b) are similar, this suggests that the observed outcome may be causally related to the intervention.

Untreated Control Group Design with Dependent Pretest and Posttest Samples Using a Double Pretest:

In this design, the pretests are administered at two different times. The main advantage of this design is that it controls for potentially different time-varying confounding effects in the intervention group and the comparison group. In our example, measuring points O1 and O2 would allow for the assessment of time-dependent changes in pharmacy costs, e.g., due to differences in experience of residents, preintervention between the intervention and control group, and whether these changes were similar or different.

Untreated Control Group Design with Dependent Pretest and Posttest Samples Using Switching Replications:

With this study design, the researcher administers an intervention at a later time to a group that initially served as a nonintervention control. The advantage of this design over design C2 is that it demonstrates reproducibility in two different settings. This study design is not limited to two groups; in fact, the study results have greater validity if the intervention effect is replicated in different groups at multiple times. In the example of a pharmacy order-entry system, one could implement or intervene in the MICU and then at a later time, intervene in the SICU. This latter design is often very applicable to medical informatics where new technology and new software is often introduced or made available gradually.

Interrupted Time-Series Designs

An interrupted time-series design is one in which a string of consecutive observations equally spaced in time is interrupted by the imposition of a treatment or intervention. The advantage of this design is that with multiple measurements both pre- and postintervention, it is easier to address and control for confounding and regression to the mean. In addition, statistically, there is a more robust analytic capability, and there is the ability to detect changes in the slope or intercept as a result of the intervention in addition to a change in the mean values. 18 A change in intercept could represent an immediate effect while a change in slope could represent a gradual effect of the intervention on the outcome. In the example of a pharmacy order-entry system, O1 through O5 could represent monthly pharmacy costs preintervention and O6 through O10 monthly pharmacy costs post the introduction of the pharmacy order-entry system. Interrupted time-series designs also can be further strengthened by incorporating many of the design features previously mentioned in other categories (such as removal of the treatment, inclusion of a nondependent outcome variable, or the addition of a control group).

Systematic Review Results

The results of the systematic review are in Table 3 . In the four-year period of JAMIA publications that the authors reviewed, 25 quasi-experimental studies among 22 articles were published. Of these 25, 15 studies were of category A, five studies were of category B, two studies were of category C, and no studies were of category D. Although there were no studies of category D (interrupted time-series analyses), three of the studies classified as category A had data collected that could have been analyzed as an interrupted time-series analysis. Nine of the 25 studies (36%) mentioned at least one of the potential limitations of the quasi-experimental study design. In the four-year period of IJMI publications reviewed by the authors, nine quasi-experimental studies among eight manuscripts were published. Of these nine, five studies were of category A, one of category B, one of category C, and two of category D. Two of the nine studies (22%) mentioned at least one of the potential limitations of the quasi-experimental study design.

Systematic Review of Four Years of Quasi-designs in JAMIA

JAMIA = Journal of the American Medical Informatics Association; IJMI = International Journal of Medical Informatics.

Could have been analyzed as an interrupted time-series design.

In addition, three studies from JAMIA were based on a counterbalanced design. A counterbalanced design is a higher order study design than other studies in category A. The counterbalanced design is sometimes referred to as a Latin-square arrangement. In this design, all subjects receive all the different interventions but the order of intervention assignment is not random. 19 This design can only be used when the intervention is compared against some existing standard, for example, if a new PDA-based order entry system is to be compared to a computer terminal–based order entry system. In this design, all subjects receive the new PDA-based order entry system and the old computer terminal-based order entry system. The counterbalanced design is a within-participants design, where the order of the intervention is varied (e.g., one group is given software A followed by software B and another group is given software B followed by software A). The counterbalanced design is typically used when the available sample size is small, thus preventing the use of randomization. This design also allows investigators to study the potential effect of ordering of the informatics intervention.

Although quasi-experimental study designs are ubiquitous in the medical informatics literature, as evidenced by 34 studies in the past four years of the two informatics journals, little has been written about the benefits and limitations of the quasi-experimental approach. As we have outlined in this paper, a relative hierarchy and nomenclature of quasi-experimental study designs exist, with some designs being more likely than others to permit causal interpretations of observed associations. Strengths and limitations of a particular study design should be discussed when presenting data collected in the setting of a quasi-experimental study. Future medical informatics investigators should choose the strongest design that is feasible given the particular circumstances.

Rothman KJ Greenland S . Modern epidemiology . Philadelphia : Lippincott–Raven Publishers , 1998 .

Google Scholar

Google Preview

Hennekens CH Buring JE . Epidemiology in medicine . Boston : Little, Brown , 1987 .

Szklo M Nieto FJ . Epidemiology: beyond the basics . Gaithersburg, MD : Aspen Publishers , 2000 .

Shadish WR Cook TD Campbell DT . Experimental and quasi-experimental designs for generalized causal inference . Boston : Houghton Mifflin , 2002 .

Trochim WMK . The research methods knowledge base . Cincinnati : Atomic Dog Publishing , 2001 .

Cook TD Campbell DT . Quasi-experimentation: design and analysis issues for field settings . Chicago : Rand McNally Publishing Company , 1979 .

MacLehose RR Reeves BC Harvey IM Sheldon TA Russell IT Black AM . A systematic review of comparisons of effect sizes derived from randomised and non-randomised studies . Health Technol Assess 2000 ; 4 : 1 – 154 .

Shadish WR Heinsman DT . Experiments versus quasi-experiments: do they yield the same answer? NIDA Res Monogr 1997 ; 170 : 147 – 64 .

Grimshaw J Campbell M Eccles M Steen N . Experimental and quasi-experimental designs for evaluating guideline implementation strategies . Fam Pract 2000 ; 17 ( Suppl 1 ): S11 – 6 .

Zwerling C Daltroy LH Fine LJ Johnston JJ Melius J Silverstein BA . Design and conduct of occupational injury intervention studies: a review of evaluation strategies . Am J Ind Med 1997 ; 32 : 164 – 79 .

Haux RKC , editor. Yearbook of medical informatics 2005 . Stuttgart : Schattauer Verlagsgesellschaft , 2005 , p 563 .

Morton V Torgerson DJ . Effect of regression to the mean on decision making in health care . BMJ 2003 ; 326 : 1083 – 4 .

Bland JM Altman DG . Regression towards the mean . BMJ 1994 ; 308 : 1499 .

Bland JM Altman DG . Some examples of regression towards the mean . BMJ 1994 ; 309 : 780 .

Guyatt GH Haynes RB Jaeschke RZ Cook DJ Green L Naylor CD et al.  . Users' guides to the medical literature: XXV. Evidence-based medicine: principles for applying the users' guides to patient care. Evidence-Based Medicine Working Group . JAMA 2000 ; 284 : 1290 – 6 .

Harris RP Helfand M Woolf SH Lohr KN Mulrow CD Teutsch SM et al.  . Current methods of the US Preventive Services Task Force: a review of the process . Am J Prev Med 2001 ; 20 : 21 – 35 .

Harbour R Miller J . A new system for grading recommendations in evidence based guidelines . BMJ 2001 ; 323 : 334 – 6 .

Wagner AK Soumerai SB Zhang F Ross-Degnan D . Segmented regression analysis of interrupted time series studies in medication use research . J Clin Pharm Ther 2002 ; 27 : 299 – 309 .

Campbell DT . Counterbalanced design . In: Company RMCP , editor. Experimental and Quasiexperimental Designs for Research . Chicago : Rand-McNally College Publishing Company , 1963 , 50 – 5 .

Staggers N Kobus D . Comparing response time, errors, and satisfaction between text-based and graphical user interfaces during nursing order tasks . J Am Med Inform Assoc 2000 ; 7 : 164 – 76 .

Schriger DL Baraff LJ Buller K Shendrikar MA Nagda S Lin EJ et al.  . Implementation of clinical guidelines via a computer charting system: effect on the care of febrile children less than three years of age . J Am Med Inform Assoc 2000 ; 7 : 186 – 95 .

Patel VL Kushniruk AW Yang S Yale JF . Impact of a computer-based patient record system on data collection, knowledge organization, and reasoning . J Am Med Inform Assoc 2000 ; 7 : 569 – 85 .

Borowitz SM . Computer-based speech recognition as an alternative to medical transcription . J Am Med Inform Assoc 2001 ; 8 : 101 – 2 .

Patterson R Harasym P . Educational instruction on a hospital information system for medical students during their surgical rotations . J Am Med Inform Assoc 2001 ; 8 : 111 – 6 .

Rocha BH Christenson JC Evans RS Gardner RM . Clinicians' response to computerized detection of infections . J Am Med Inform Assoc 2001 ; 8 : 117 – 25 .

Lovis C Chapko MK Martin DP Payne TH Baud RH Hoey PJ et al.  . Evaluation of a command-line parser-based order entry pathway for the Department of Veterans Affairs electronic patient record . J Am Med Inform Assoc 2001 ; 8 : 486 – 98 .

Hersh WR Junium K Mailhot M Tidmarsh P . Implementation and evaluation of a medical informatics distance education program . J Am Med Inform Assoc 2001 ; 8 : 570 – 84 .

Makoul G Curry RH Tang PC . The use of electronic medical records: communication patterns in outpatient encounters . J Am Med Inform Assoc 2001 ; 8 : 610 – 5 .

Ruland CM . Handheld technology to improve patient care: evaluating a support system for preference-based care planning at the bedside . J Am Med Inform Assoc 2002 ; 9 : 192 – 201 .

De Lusignan S Stephens PN Adal N Majeed A . Does feedback improve the quality of computerized medical records in primary care? J Am Med Inform Assoc 2002 ; 9 : 395 – 401 .

Mekhjian HS Kumar RR Kuehn L Bentley TD Teater P Thomas A et al.  . Immediate benefits realized following implementation of physician order entry at an academic medical center . J Am Med Inform Assoc 2002 ; 9 : 529 – 39 .

Ammenwerth E Mansmann U Iller C Eichstadter R . Factors affecting and affected by user acceptance of computer-based nursing documentation: results of a two-year study . J Am Med Inform Assoc 2003 ; 10 : 69 – 84 .

Oniki TA Clemmer TP Pryor TA . The effect of computer-generated reminders on charting deficiencies in the ICU . J Am Med Inform Assoc 2003 ; 10 : 177 – 87 .

Liederman EM Morefield CS . Web messaging: a new tool for patient-physician communication . J Am Med Inform Assoc 2003 ; 10 : 260 – 70 .

Rotich JK Hannan TJ Smith FE Bii J Odero WW Vu N Mamlin BW et al.  . Installing and implementing a computer-based patient record system in sub-Saharan Africa: the Mosoriot Medical Record System . J Am Med Inform Assoc 2003 ; 10 : 295 – 303 .

Payne TH Hoey PJ Nichol P Lovis C . Preparation and use of preconstructed orders, order sets, and order menus in a computerized provider order entry system . J Am Med Inform Assoc 2003 ; 10 : 322 – 9 .

Hoch I Heymann AD Kurman I Valinsky LJ Chodick G Shalev V . Countrywide computer alerts to community physicians improve potassium testing in patients receiving diuretics . J Am Med Inform Assoc 2003 ; 10 : 541 – 6 .

Laerum H Karlsen TH Faxvaag A . Effects of scanning and eliminating paper-based medical records on hospital physicians' clinical work practice . J Am Med Inform Assoc 2003 ; 10 : 588 – 95 .

Devine EG Gaehde SA Curtis AC . Comparative evaluation of three continuous speech recognition software packages in the generation of medical reports . J Am Med Inform Assoc 2000 ; 7 : 462 – 8 .

Dunbar PJ Madigan D Grohskopf LA Revere D Woodward J Minstrell J et al.  . A two-way messaging system to enhance antiretroviral adherence . J Am Med Inform Assoc 2003 ; 10 : 11 – 5 .

Lenert L Munoz RF Stoddard J Delucchi K Bansod A Skoczen S et al.  . Design and pilot evaluation of an Internet smoking cessation program . J Am Med Inform Assoc 2003 ; 10 : 16 – 20 .

Koide D Ohe K Ross-Degnan D Kaihara S . Computerized reminders to monitor liver function to improve the use of etretinate . Int J Med Inf 2000 ; 57 : 11 – 9 .

Gonzalez-Heydrich J DeMaso DR Irwin C Steingard RJ Kohane IS Beardslee WR . Implementation of an electronic medical record system in a pediatric psychopharmacology program . Int J Med Inf 2000 ; 57 : 109 – 16 .

Anantharaman V Swee Han L . Hospital and emergency ambulance link: using IT to enhance emergency pre-hospital care . Int J Med Inf 2001 ; 61 : 147 – 61 .

Chae YM Heon Lee J Hee Ho S Ja Kim H Hong Jun K Uk Won J . Patient satisfaction with telemedicine in home health services for the elderly . Int J Med Inf 2001 ; 61 : 167 – 73 .

Lin CC Chen HS Chen CY Hou SM . Implementation and evaluation of a multifunctional telemedicine system in NTUH . Int J Med Inf 2001 ; 61 : 175 – 87 .

Mikulich VJ Liu YC Steinfeldt J Schriger DL . Implementation of clinical guidelines through an electronic medical record: physician usage, satisfaction and assessment . Int J Med Inf 2001 ; 63 : 169 – 78 .

Hwang JI Park HA Bakken S . Impact of a physician's order entry (POE) system on physicians' ordering patterns and patient length of stay . Int J Med Inf 2002 ; 65 : 213 – 23 .

Park WS Kim JS Chae YM Yu SH Kim CY Kim SA et al.  . Does the physician order-entry system increase the revenue of a general hospital? Int J Med Inf 2003 ; 71 : 25 – 32 .

Dr. Harris was supported by NIH grants K23 AI01752-01A1 and R01 AI60859-01A1. Dr. Perencevich was supported by a VA Health Services Research and Development Service (HSR&D) Research Career Development Award (RCD-02026-1). Dr. Finkelstein was supported by NIH grant RO1 HL71690.

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Research Methodologies Guide

• Action Research
• Bibliometrics
• Case Studies
• Content Analysis
• Digital Scholarship This link opens in a new window
• Documentary
• Ethnography
• Focus Groups
• Grounded Theory
• Life Histories/Autobiographies
• Longitudinal
• Participant Observation
• Qualitative Research (General)

Quasi-Experimental Design

• Usability Studies

Quasi-Experimental Design is a unique research methodology because it is characterized by what is lacks. For example, Abraham & MacDonald (2011) state:

" Quasi-experimental research is similar to experimental research in that there is manipulation of an independent variable. It differs from experimental research because either there is no control group, no random selection, no random assignment, and/or no active manipulation. "

This type of research is often performed in cases where a control group cannot be created or random selection cannot be performed. This is often the case in certain medical and psychological studies. 

For more information on quasi-experimental design, review the resources below: 

Where to Start

Below are listed a few tools and online guides that can help you start your Quasi-experimental research. These include free online resources and resources available only through ISU Library.

• Quasi-Experimental Research Designs by Bruce A. Thyer This pocket guide describes the logic, design, and conduct of the range of quasi-experimental designs, encompassing pre-experiments, quasi-experiments making use of a control or comparison group, and time-series designs. An introductory chapter describes the valuable role these types of studies have played in social work, from the 1930s to the present. Subsequent chapters delve into each design type's major features, the kinds of questions it is capable of answering, and its strengths and limitations.
• Experimental and Quasi-Experimental Designs for Research by Donald T. Campbell; Julian C. Stanley. Call Number: Q175 C152e Written 1967 but still used heavily today, this book examines research designs for experimental and quasi-experimental research, with examples and judgments about each design's validity.

Online Resources

• Quasi-Experimental Design From the Web Center for Social Research Methods, this is a very good overview of quasi-experimental design.
• Experimental and Quasi-Experimental Research From Colorado State University.
• Quasi-experimental design--Wikipedia, the free encyclopedia Wikipedia can be a useful place to start your research- check the citations at the bottom of the article for more information.
• << Previous: Qualitative Research (General)
• Next: Sampling >>
• Last Updated: Aug 12, 2024 4:07 PM
• URL: https://instr.iastate.libguides.com/researchmethods

Experimental vs Quasi-Experimental Design: Which to Choose?

Here’s a table that summarizes the similarities and differences between an experimental and a quasi-experimental study design:

What is a quasi-experimental design?

A quasi-experimental design is a non-randomized study design used to evaluate the effect of an intervention. The intervention can be a training program, a policy change or a medical treatment.

Unlike a true experiment, in a quasi-experimental study the choice of who gets the intervention and who doesn’t is not randomized. Instead, the intervention can be assigned to participants according to their choosing or that of the researcher, or by using any method other than randomness.

Having a control group is not required, but if present, it provides a higher level of evidence for the relationship between the intervention and the outcome.

(for more information, I recommend my other article: Understand Quasi-Experimental Design Through an Example ) .

Examples of quasi-experimental designs include:

• One-Group Posttest Only Design
• Static-Group Comparison Design
• One-Group Pretest-Posttest Design
• Separate-Sample Pretest-Posttest Design

What is an experimental design?

An experimental design is a randomized study design used to evaluate the effect of an intervention. In its simplest form, the participants will be randomly divided into 2 groups:

• A treatment group: where participants receive the new intervention which effect we want to study.
• A control or comparison group: where participants do not receive any intervention at all (or receive some standard intervention).

Randomization ensures that each participant has the same chance of receiving the intervention. Its objective is to equalize the 2 groups, and therefore, any observed difference in the study outcome afterwards will only be attributed to the intervention – i.e. it removes confounding.

(for more information, I recommend my other article: Purpose and Limitations of Random Assignment ).

Examples of experimental designs include:

• Posttest-Only Control Group Design
• Pretest-Posttest Control Group Design
• Solomon Four-Group Design
• Matched Pairs Design
• Randomized Block Design

When to choose an experimental design over a quasi-experimental design?

Although many statistical techniques can be used to deal with confounding in a quasi-experimental study, in practice, randomization is still the best tool we have to study causal relationships.

Another problem with quasi-experiments is the natural progression of the disease or the condition under study — When studying the effect of an intervention over time, one should consider natural changes because these can be mistaken with changes in outcome that are caused by the intervention. Having a well-chosen control group helps dealing with this issue.

So, if losing the element of randomness seems like an unwise step down in the hierarchy of evidence, why would we ever want to do it?

This is what we’re going to discuss next.

When to choose a quasi-experimental design over a true experiment?

The issue with randomness is that it cannot be always achievable.

So here are some cases where using a quasi-experimental design makes more sense than using an experimental one:

• If being in one group is believed to be harmful for the participants , either because the intervention is harmful (ex. randomizing people to smoking), or the intervention has a questionable efficacy, or on the contrary it is believed to be so beneficial that it would be malevolent to put people in the control group (ex. randomizing people to receiving an operation).
• In cases where interventions act on a group of people in a given location , it becomes difficult to adequately randomize subjects (ex. an intervention that reduces pollution in a given area).
• When working with small sample sizes , as randomized controlled trials require a large sample size to account for heterogeneity among subjects (i.e. to evenly distribute confounding variables between the intervention and control groups).

Further reading

• Statistical Software Popularity in 40,582 Research Papers
• Checking the Popularity of 125 Statistical Tests and Models
• Objectives of Epidemiology (With Examples)
• 12 Famous Epidemiologists and Why

• Open access
• Published: 19 August 2024

Simulated medication administration for vulnerable populations using scanning technology: a quasi-experimental pilot study

• Anne Meginniss 1 ,
• Courtney Coffey 1 &
• Kristen D. Clark   ORCID: orcid.org/0000-0001-6584-4560 1 , 2  

BMC Nursing volume  23 , Article number:  576 ( 2024 ) Cite this article

107 Accesses

Metrics details

Medication errors may occur due to shortcuts and pressures on time and resources on nurses. Nursing students are enculturated into these environments where their perceptions of norms around reporting and responding to medication errors are formative, yet simulated medication administration experiences are rarely reflective of the real-world environment. such as the standard use of medication scanning technology. The purpose of the present study is to test a pilot intervention, Medication Quick Response (QR) code scanning, and evaluate its effect on medication errors during simulation when compared to traditional simulation medication administration practices and to assess the students’ perceptions of the intervention.

We conducted a quasi-experimental, observational study involving Junior and Senior (3rd and 4th year) undergraduate, pre-licensure nursing students from Spring 2022 until Fall 2023. Seven simulations were conducted in pediatric and obstetric courses. The intervention group used non-patented, low cost QR scanning during medication administration. The control group used standard manual administration. Medication errors were measured based on the quantity, type of error, and degree of patient risk. A Qualtrics survey was used to assess the students’ perceptions of the intervention following simulation participation.

A total of 166 students participated in the study. In each course, 7 groups were assigned to the intervention and 8 were assigned to the control. More than half of the groups made at least one medication error ( n  = 17), one-third of groups ( n  = 10) made a high-risk medication error. There was no statistically meaningful difference in the rate, type, or potential patient risk of medication errors between the intervention and control groups. The majority of participants ( n  = 53) felt that QR scanning more closely mimicked medication administration in clinical settings. Half of the participants responded that it improved their safety practices ( n  = 37).

Conclusions

The results of this pilot study indicate that while there is a high risk for error among pre-licensure nursing students, the use of QR scanning did not increase the risk of medication errors. The next study iteration will build upon these pilot findings to integrate the use of embedded medication errors, time management tasks, and a multi-site implementation.

Peer Review reports

Introduction

The Academy of Managed Care Pharmacy (AMCP) estimates that medication errors harm 1.5 million patients per year in the United States (US) and are responsible for up to 98,000 patient deaths annually [ 1 ]. Medication errors pose significant risks to patient safety and are a prevalent concern in healthcare settings worldwide. Nurses play a pivotal role in medication safety as they are the primary healthcare professional who administers medication, making them the final line of protection between patients and medication errors. Before the COVID19 pandemic, the global nursing workforce was already considered well below demand, with projected growth insufficient to meet healthcare system needs due to the retirement of existing nurses and an aging population [ 2 ]. During the COVID19 pandemic, an unprecedented workforce strain occurred, with health systems becoming overwhelmed and healthcare staff contracting COVID19 at high rates, some of whom experienced post-COVID syndrome which further impeded their ability to return to work at full capacity [ 3 , 4 ] The increasing healthcare system strain, chronic understaffing, pressures to meet increasingly acute patient needs, and throughput metrics have resulted in challenges to nurses’ ability to safely administer medications.

Medication safety practices are a cornerstone of nursing education, and students are ingrained with the 5 rights of medication administration to reduce the risk of such errors. These rights include: right patient, right drug, the right dose, the right route, and the right time. However, this approach has long been critiqued for lacking the specificity and depth to accurately depict the complexity of medication errors [ 5 , 6 ]. An error can occur at many different points in the administration continuum. Specifically, they can occur at the time a medication order is placed, during its preparation with the pharmacy, when the nurse retrieves the medication from the medication dispensing system, when the nurse is preparing the medication to be delivered, or during its administration to the patient. In addition to the error’s place in the medication administration continuum, there is variation in the types of medication errors that can occur. The most common types of medication errors observed in hospital settings are timing errors (early or late doses), omission errors (doses missed), and dosage errors (too small or too large; [ 7 , 8 ]). High-profile cases of medication errors resulting in significant patient harm have entered the public consciousness and, in one instance, resulted in the rare occurrence of a nurse receiving criminal charges in the US [ 9 , 10 ]. While conversations across healthcare have taken place around the relationship between patient safety and strained staffing environments, there has been less discussion surrounding the enculturation of prelicensure nursing students to normalized workarounds and shortcuts in patient care delivery.

Medication safety is a primary component of nursing education. However, witnessing senior nurses or preceptors engaging in workarounds or substandard medication safety practices normalizes these practices for pre-licensure and recently graduated nurses [ 11 ]. Novice nurses may not have the fortitude to question a senior coworker’s practice given the power gradient that exists between them [ 12 ]. It is difficult to know the exact rate of medication errors made by recently graduated nurses, as this number is likely underreported, however, a survey found that 55% of recent graduate nurses reported having made a medication error [ 22 ]. Additionally, a study of pre-licensure nursing students using simulation found that by the end of four semesters, 80% of participants were not engaging in safe medication administration practices [ 13 ]. It is possible that this high rate of unsafe medication administration practices observed in the study could be due to a lack of realism in simulated medication administration [ 14 ], leading students to perceive the activity as having little impact on real-world patient care. This suggests a need for recurrent education and evaluation of safe medication practices throughout the curriculum with an emphasis on the replication of real-life practices.

Studies have demonstrated that nurses spend approximately 40% of their time at work focused on medication management [ 15 ]. It is critical to examine whether adequate time is spent on education surrounding medication safety and, more importantly, to ask if the education provided is effective. Simulation has been used to create learning opportunities for nursing students to practice medication administration. Engaging in medication administration during high-fidelity simulations has been shown to increase nursing student’s knowledge related to medication safety [ 16 ]. However, simulation has been described as limited in its capacity to incorporate all the features of real clinical settings. The aspect of realism is a key component of fidelity and one of the cornerstones of evidence-based simulation practice [ 14 , 17 ]. Realism in simulation, through physical, emotional, and psychological approaches, is associated with higher competency evaluations and engagement among nursing students. Yet realism in application to medication administration has lagged behind clinical practices in favor of more manual approaches. Current practices rely heavily on memorization and do not use resources commonly available in clinical settings. For example, students are often tasked with preparing large numbers of notecards with extensive details on each medication that is assigned to each patient [ 18 ], yet integration of currently available technology, such as smartphones or medication barcode scanning, is underutilized. Such technologies have been shown to have educational benefits, such as improved collaboration with peers and mentorship in clinical settings [ 19 ], as a tool to deliver medication administration information [ 20 , 21 ], and an increase in perceived clinical preparedness [ 22 , 23 ]. Incorporation of technology that is readily available in clinical settings into simulation provides a pathway for students to investigate the realities of practice and explore technology’s potential limitations in a controlled setting.

Incorporating real-life tools into the medication administration process offers the opportunity for students to identify the limitations of that technology and to encounter circumstances where they must question the accuracy, or respond to irregularities as they arise, thereby increasing their capacity for critical thinking and adaptation in real-world environments. However, the software and tools required to integrate this technology into educational simulation settings are costly, inefficient, partially functional, or incompatible with existing technologies. Therefore, the purpose of the present study is to test a pilot intervention, Medication Quick Response (QR) code scanning, and evaluate its effect on medication errors during simulation when compared to traditional simulation medication administration practices with pre-licensure, undergraduate nursing students. We will also evaluate the students’ perception of the intervention for future implementation in a larger-scale study.

Materials and methods

Recruitment and procedures.

A quasi-experimental, observational study was used to address the present aims. Junior and Senior prelicensure nursing students enrolled in pediatrics and obstetrics courses from Spring 2022 until Fall 2023 were recruited to participate. Pediatrics and obstetrics courses were chosen for this intervention’s pilot because medication errors are particularly concerning in the context of these vulnerable populations [ 8 , 24 ]. Medication administration for these populations can be particularly complex and an error can have more severe effects on children, pregnant persons, and fetuses.

The course simulation sections for pediatrics and obstetrics courses were assigned as either control or interventions based on alternating weeks and where they were placed during course registration. Groups registered to week A were placed in the control, and groups registered to week B were placed in the intervention. Simulation groups were comprised of four to six students who worked through the simulation scenario collaboratively. Medication errors were subsequently analyzed based on group performance as opposed to individual participants.

Before the simulation

Before the simulation, students were provided with preparation materials, which included access to the patient chart and protocols that were utilized during the scenario. Medications that were available during the simulation were listed and students had the opportunity to look up medications before and during the scenario. A guided preparation homework assignment was completed by all students before the simulation. The purpose of this assignment was to review content from the course and to highlight important information that would be addressed within the simulation. Once the students arrived at the lab on the day of the simulation, a pre-brief was completed. During the pre-brief, the scenario was explained in further detail and roles were assigned. Students had the opportunity to ask questions before the initiation of the simulation.

Simulation scenarios

The simulation scenarios used in this study were developed per the INACSL Standards of Best Practice [ 17 , 25 ]. In the obstetrical health course, two high-fidelity simulation scenarios were used involving medication administration to mother and baby dyads (i.e., Brenda and Renee). In the pediatrics course, five high-fidelity simulation scenarios were used involving medication administration (i.e., Sam, Sabina, Jack, Charlie, and Abigail). All simulation scenarios took place in a simulated inpatient hospital setting with a laptop that provided access to the patient’s chart and medication administration record through DocuCare [ 26 ]. Participants engaged with one scenario in each session. In the intervention groups, the patient wristband and medications for the simulation were labeled with barcodes. In the control groups, standard manual administration processes were followed (i.e., no barcodes were provided on medications or patient wristbands). All groups had access to the simulation case, including medications, before participating in the scenario. The simulation scenarios contained between three and six medications to be administered. All scenarios except one (Charlie) contained at least one high-complexity medication to be administered (e.g., ceftriaxone to be administered piggybacked to intravenous fluids which requires drug compatibility verification, dosage calculation, and to program the pump). A full description of the medications by scenario and complexity can be found in Supplemental Table 2 . No medication errors were embedded into the scenarios.

Measurement

Demographics.

Participants were asked to indicate which academic year they were currently enrolled in (i.e., Junior or Senior). Participants were also asked whether they had previous experience with medication administration using scanning technology, indicating yes or no.

Intervention

Current tools available for nursing education pose barriers to the broad implementation of medication administrative technologies representative of real-world clinical practice. Electronic health record systems developed for nursing education are cumbersome and labor-intensive to integrate medication and wristband scanning capabilities. Alerts for mis-scanning medications are unreliable, providing a false sense of safety and difficult for instructors to observe the information the students are receiving. The programs are also costly, a challenge for many nursing programs to obtain. For the present study, Medication Quick Response (QR) code scanning was tested as a non-patented, low-cost method to replicate traditional medication barcode scanning in the simulation setting. QR codes were created using a free QR-generating website [ 27 ] and placed on the patient’s wristband and medications used within the simulation scenarios YouTube shorts videos were created by study personnel for use during the simulation (Supplemental Table 1 ). Upon scanning the barcode on the patient identification band with their mobile phone, a YouTube short video displaying the patient chart played. When the participants scanned the medication barcodes, another YouTube shorts video was played with medication information. Students also could view the medication order and chart using the provided laptop in the patient’s room. The control groups did not receive barcode scanning and administered medication per standard processes.

• Medication errors

Faculty members oversaw each simulation group to assess for medication errors. Medication errors were measured by quantity, type of error, and category of potential patient risk. The types of medication errors were defined based on the U.S. Food and Drug Administration’s healthcare professional reporting form [ 28 ] and included: compatibility error, incorrect administration technique, incorrect administration time, known allergy, reconstitution error, wrong dose, wrong medication, wrong patient, wrong route, and unsafe to administer. Please see Table  1 for the full list of error types and their operational definitions. After making a medication error, faculty used the National Coordinating Council Medication Error Reporting and Prevention (NCC MERP) Index to determine the potential patient risk imposed by the error. The NCC MERP assigns an ordinal range of categories (A = near miss event, to I = error causing/contributing to patient death) to medication errors. This index is intended for use in clinical settings with real patients, therefore we used the following categories and numbered them from 1 to 4: A- near miss, B- error did not reach patient, C- reached patient, but no harm, D- patient required monitoring or intervention, but no significant harm). This variable was dichotomized as low potential patient risk (less than 3) and high potential patient risk (3 or more).

Students’ perceptions

Participants were provided a brief Qualtrics survey that asked three questions about their perceptions of the intervention. Students were asked, “If you used the QR code scanning, did you feel it improved your medication administration during simulation?” with a 3-point Likert-type scale for responses (i.e., yes, maybe, and no). Participants were also asked, “If you used the QR code scanning in simulation, do you feel it simulated medication scanning in the clinical setting?” with a 3-point Likert-type response. Students were also asked “Do you think the QR code scanning prevented (or could have prevented) a medication error during the simulations?“ with the same response options. Lastly, an open-text response question was provided, asking students to provide further feedback on their experiences in the simulations.

Descriptive statistics were used to describe the characteristics of the simulation groups and observed medication errors. Mann-Whitney U-tests were used to analyze data for differences between intervention and control groups with a significance threshold of p <. 05. Open-text responses related to students’ perceptions of the simulations were analyzed using thematic analysis [ 29 ]. Two research personnel evaluated responses and coded inductively. Initial codes were then evaluated to identify final themes.

A total 178 (32 groups) students completed simulation scenarios in obstetrics and pediatrics courses across two semesters. Initially, there were eight intervention and eight control groups per course. Two intervention groups were dropped from the final analysis, one from each course, because of declined informed consent. A total of 166 students, divided into 30 groups, were included in the final sample. Seven groups in each course received the intervention, with the remaining eight acting as controls for a total of 14 intervention groups and 16 controls.

Approximately 56% ( n  = 17) of groups made at least one error. The operational definitions can be found in Table  1 . The most common error observed was incorrect medication administration technique (53.3%, n  = 22). One-third of participants ( n  = 10) made an error that posed a high potential patient risk. Differences between control and intervention groups regarding the rate of errors, type of errors, and risk potential were examined (Table  2 ).

No statistically meaningful difference in the number, type, or potential patient risk of medication errors between intervention and control groups was observed (Table  2 ). Further analysis was performed to examine group differences within each course (i.e., obstetrics and pediatrics), and found no statistically meaningful differences in the number, type, or potential patient risk of medication errors between intervention and control groups (Table  2 ).

Sixty-six students (40.9% response rate) completed the survey assessing their perceptions of the intervention at the end of the semester. Fifty-nine (86.7%) students had previous experience using QR code scanning technology. When asked if they felt QR code medication scanning improved their medication safety practices, 54.4% responded “yes” ( n  = 37). Approximately three-quarters ( n  = 53) felt, “yes, it simulated” or “somewhat simulated” medication scanning in the clinical setting. When asked “do you think the QR code scanning prevented (or could have prevented) a medication error during the simulations?”, 85.9% ( n  = 49) responded “yes” or “somewhat.”

Students’ perceptions: qualitative

Students were provided an open-text box to provide further feedback on their experiences in the simulations. Responses were grouped into themes: replicated realistic clinical medication scanning and supported critical thinking .

Replicated realistic clinical medication scanning

This theme was characterized by students describing similarities between the intervention and clinical medication scanning. One student stated, “this was a great simulation experience! QR codes felt more like real life and have double checks.”

Supported critical thinking

This theme was characterized by students describing how the simulation with medication administration improved their critical thinking related to medication administration due to technology. One student stated, “I think scanning helped us think through the medication administration before we did it.”

The purpose of the present study was to test a pilot intervention, the implementation of medication administration technology (e.g., medication barcode scanning), and evaluate its effect on medication errors during simulation when compared to traditional simulation medication administration with pre-licensure, undergraduate nursing students.

It was found that the implementation of QR code medication scanning during simulations was not statistically different in terms of error rates, types, or potential risk to patient safety when compared to traditional simulation of medication administration. While improved medication safety was not observed, there was no increased risk of error, suggesting that the incorporation of QR scanning should be explored for inclusion as standard practice in simulation settings.

The study also aimed to evaluate students’ perceptions of this intervention for future implementation in a larger-scale study. Most students had experience with medication scanning before the simulation, indicating that the use of medication scanning in the simulation would align with real-world clinical environments. Yet, the lack of integration is evidence of a considerable gap between simulation experiences and clinical settings. These participant perspectives further support the urgency to bridge differences between the two environments. The results of this study provide support for the use of Medication Quick Response (QR) codes as a low-cost, efficient, and accessible tool to accomplish this goal. Additionally, this study exhibits how realism can be improved through the use of medication scanning technologies [ 21 , 23 ], even with limited resources.

Within the open-text responses obtained from participants at the end of their participation in the study, the use of QR code scanning to simulate medication administration barcode scanning was perceived to encourage critical thinking. However, participants did not specify how . It is possible that students perceived this use of critical thinking in relation to the medication complexity and not the scanning itself. Alternatively, this could be related to the standardization of medication administration safety practices and the simulation of students’ real-world experiences where they are required to utilize critical thinking in medication administration broadly.

Limitations

While the present study was a pilot, there are limitations to note. The sample size was relatively small and from a single study site, and therefore, is not representative of the pre-licensure nursing student population. Additionally, there was a lack of randomization and no allocation concealment within the study. The simulation scenarios also did not include embedded errors, which would mimic real-world applications. An example of this would be purposefully having a barcode that did not scan. The utilization of embedded errors would further the utilization of critical thinking skills to determine appropriate next steps.

Next steps for implementation

The current pilot study indicates that the inclusion of QR scanning during simulation medication administration did not increase the risk of medication error, providing foundational information which the next study iteration can build from. A feasibility study is planned to advance the findings of the present study through the addition of embedded medication errors (e.g., barcodes that do not scan, barcodes that scan as the wrong medication), time management evaluations for polypharmacy (e.g., on-time parameters, medication prioritization), and questioning individuals of actual or perceived authority (e.g., provider, pharmacist). Embedded distractions, such as a family member in the room asking questions during medication administration, would also increase complexity in a manner that mimics real-world care environments and factors that increase the risk of medication errors [ 23 ] and are also a feature that is planned for feasibility testing.

With these added layers of complexity, an assessment of feasibility and the appropriateness of scaling these features to students’ level of learning and skills is needed. Through feasibility testing of embedded features within simulated medication administration, a recommending scaling approach can be developed based on students’ level of education and experience, but also integrated across the nursing curriculum.

Future directions

As nursing education advances, simulation offers a unique opportunity for the development of skills but also for the mindset of future practicing nurses. Paulo Freire described the role of oppression and learning, where students are in positions of little power in their schools and universities, an experience that carries through to the clinical settings for nursing students [ 30 , 31 ]. Shifting the view of nursing students and novice nurses as inferior, passive recipients of knowledge to active participants who are capable of creating a culture of change allows for enriched, meaningful learning experiences built on the foundation of critical thinking skills that can carry into complex clinical experiences, such as medication administration. This can be accomplished through future research investigating increased complexity in medication administration and by reimagining how outcomes for the simulations are defined.

In addition to the steps outlined as planned for implementation following this present study, additional approaches to integrating medication administration complexity include the use of multiple patient simulations occurring at the same time to expose students to the administration and prioritization of multiple medications [ 22 ]. Research focused on understanding students’ reliance on scanning technology when administering medications would inform areas where complexity can be enhanced and reliance on technology can be challenged [ 32 , 33 ]. Integration of interpersonal professional scenarios forms another opportunity for medication administration complexity development. Examples of interpersonal professional scenarios could include circumstances requiring students to question the safety or appropriateness of medication orders or a situation where students must respond to an observed medication error or safety concern made by a colleague.

The use of simulation as a tool to empower and advance critical thinking calls for a reimagining of successful simulation outcomes. Evaluation of simulation performance often uses a pass/fail approach, where students fail if they make a medication error. However, medication near misses and errors will occur in the clinical setting. Expanding the definition of success to include an appropriate response to a medication error, such as reporting and documentation, would aid students in learning how to respond to such events and enculturate them to a process improvement practice philosophy. These varying approaches, from complexity to expanding the definitions of success, could be studied toward the development of an operationalized approach to simulation medication administration across the spectrum of nursing education so that medication admiration experiences can be scaled by difficulty and level of learning, integrated across cohorts and programs.

The present findings reveal a concerning prevalence of errors, even amongst the groups that utilized the QR code medication scanning method. The use of QR scanning during simulated medication administration was, however, found to have no difference in medication errors when compared to standard practices. Participants reported that the use of QR scanning more closely resembled their clinical settings and that they perceived a greater use of critical thinking skills. This pilot provides initial evidence that medication barcode scanning can be implemented with low resource tools and should continue to be explored for implementation across nursing curricula in a movement toward greater realism in nursing simulation related to medication administration practices. These findings underscore the importance of advancing simulation practices to address medication errors within nursing education, particularly in highly complex patient populations such as pediatrics and obstetrics.

Data availability

The datasets generated and/or analysed during the current study are not publicly available due conditions of the data management agreement to protect participant privacy. The data that support the findings of this study are available upon reasonable request from the authors.

Academy of Managed Care Pharmacy. 2019 [cited 2024 Apr 10]. Medication Errors. https://www.amcp.org/about/managed-care-pharmacy-101/concepts-managed-care-pharmacy/medication-errors

World Health Organization. State of the world’s nursing 2020: Investing in education, jobs, and leadership. Geneva. 2020. https://iris.who.int/bitstream/handle/10665/331677/9789240003279-eng.pdf?sequence=1

Nguyen LH, Drew DA, Graham MS, Joshi AD, Guo CG, Ma W, et al. Risk of COVID-19 among front-line health-care workers and the general community: a prospective cohort study. Lancet Public Health. 2020;5(9):e475–83.

Article   PubMed   PubMed Central   Google Scholar  

Cruickshank M, Brazzelli M, Manson P, Torrance N, Grant A. What is the impact of long-term COVID-19 on workers in healthcare settings? A rapid systematic review of current evidence. Ubom AEB, editor. PLOS ONE. 2024;19(3):e0299743.

Kron T. Stepping beyond the 5 rights of administering drugs. Am J Nurs. 1962;62:62–3.

CAS   PubMed   Google Scholar  

Grissinger M. The Five rights: a destination without a map. Pharm Ther. 2010;35(10):542.

Google Scholar  

Keers RN, Williams SD, Cooke J, Ashcroft DM. Prevalence and Nature of Medication Administration Errors in Health Care settings: a systematic review of direct observational evidence. Ann Pharmacother. 2013;47(2):237–56.

Article   PubMed   Google Scholar  

Alghamdi AA, Keers RN, Sutherland A, Ashcroft DM. Prevalence and nature of medication errors and preventable adverse drug events in paediatric and neonatal intensive care settings: a systematic review. Drug Saf. 2019;42(12):1423–36.

Article   CAS   PubMed   PubMed Central   Google Scholar  

Barry JS, Swanson JR, Pearlman SA. Is medical error a crime? The impact of the state v. Vaught on patient safety. J Perinatol. 2022;42(9):1271–4.

Carbajal E. Kentucky nurse involved in drug mix-up that led to patient death: Report. 2023 [cited 2024 Apr 9]. https://www.beckershospitalreview.com/legal-regulatory-issues/kentucky-nurse-involved-in-drug-mix-up-that-led-to-patient-death-report.html

Bedgood AL, Mellott S. The role of education in developing a culture of Safety through the perceptions of undergraduate nursing students: an Integrative Literature Review. J Patient Saf. 2021;17(8):e1530–6.

Aubin D, King S. Developing a culture of safety: exploring students’ perceptions of errors in an interprofessional setting. J Interprofessional Care J Interprof Care. 2015;29(6):646–8.

Schneidereith TA. Medication administration behaviors in prelicensure nursing students: a longitudinal, cohort study. Nurse Educ Pract. 2021;56:103189.

Berro EA, Dane FC, Knoesel J. Exploring the relationships among realism, engagement, and competency in simulation. Teach Learn Nurs. 2023;18(4):e241–5.

Article   Google Scholar  

Leufer T, Cleary-Holdforth J. Let’s do no harm: medication errors in nursing: part 1. Nurse Educ Pract. 2013;13(3):213–6.

Konieczny L. Using High-Fidelity Simulation to increase nursing student knowledge in Medication Administration. Teach Learn Nurs. 2016;11(4):199–203.

McDermott DS, Ludlow J, Horsley E, Meakim C. Healthcare Simulation standards of best PracticeTM prebriefing: Preparation and briefing. Clin Simul Nurs. 2021;58:9–13.

Conner BT, Anderson BS, Matutina R. Exploring the perceptions of male nursing students enrolled in an accelerated baccalaureate degree nursing program. J Nurs Educ Pract. 2016;6(8):p30.

Strandell-Laine C, Stolt M, Leino-Kilpi H, Saarikoski M. Use of mobile devices in nursing student–nurse teacher cooperation during the clinical practicum: an integrative review. Nurse Educ Today. 2015;35(3):493–9.

Siebert JN, Ehrler F, Combescure C, Lovis C, Haddad K, Hugon F, et al. A mobile device application to reduce medication errors and time to drug delivery during simulated paediatric cardiopulmonary resuscitation: a multicentre, randomised, controlled, crossover trial. Lancet Child Adolesc Health. 2019;3(5):303–11.

Orbæk J, Gaard M, Fabricius P, Lefevre RS, Møller T. Patient safety and technology-driven medication – a qualitative study on how graduate nursing students navigate through complex medication administration. Nurse Educ Pract. 2015;15(3):203–11.

Ledlow JH, Judson T, Watts P, Vance DE, Moss J. Integrating a simulated electronic medical record system and barcode medication administration into a pre-licensure nursing program. J Prof Nurs. 2022;40:38–41.

Craig SJ, Kastello JC, Cieslowski BJ, Rovnyak V. Simulation strategies to increase nursing student clinical competence in safe medication administration practices: a quasi-experimental study. Nurse Educ Today. 2021;96:104605.

White AA, Pichert JW, Bledsoe SH, Irwin C, Entman SS. Cause and Effect Analysis of Closed claims in Obstetrics and Gynecology. Obstet Gynecol. 2005;105(5 Part 1):1031.

Watts PI, McDermott DS, Alinier G, Charnetski M, Ludlow J, Horsley E, et al. Healthcare Simulation standards of best PracticeTM Simulation Design. Clin Simul Nurs. 2021;58:14–21.

DocuCare. Lippincott; [cited 2024 Jul 26]. https://www.wolterskluwer.com/en/solutions/lippincott-nursing-faculty/lippincott-docucare

QR Code Generator. | Create Your Free QR Codes. [cited 2024 Jul 26]. https://www.qr-code-generator.com/

Commissioner O of the. U.S. Food and Drug Administration (FDA). FDA. 2024 [cited 2024 Jul 25]. MedWatch Forms for FDA Safety Reporting. https://www.fda.gov/safety/medical-product-safety-information/medwatch-forms-fda-safety-reporting

Braun V, Clarke V. Thematic analysis: a practical guide. Los Angeles: SAGE; 2022.

Book   Google Scholar  

Treinen KP, Abbott-Anderson K, Kuechle L. Paolo Freire’s pedagogy of the oppressed: a Way Past Oppression for the nursing Profession. Creat Nurs. 2022;28(3):161–6.

Freire P. Pedagogy of the Oppressed*. Toward a sociology of education. Routledge; 1978.

Cohen MR, Smetzer JL. ISMP Medication Error Report Analysis: understanding human over-reliance on Technology. Hosp Pharm. 2017;52(1):7–12.

Survey shows room for improvement with three new best practices for hospitals. Institute for Safe Medication Practices; 2022 [cited 2024 Jul 23] pp. 1–5. https://www.ismp.org/resources/survey-shows-room-improvement-three-new-best-practices-hospitals

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Meginniss, A., Coffey, C. & Clark, K.D. Simulated medication administration for vulnerable populations using scanning technology: a quasi-experimental pilot study. BMC Nurs 23 , 576 (2024). https://doi.org/10.1186/s12912-024-02248-6

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Quasi-experimental study designs series—paper 5: a checklist for classifying studies evaluating the effects on health interventions—a taxonomy without labels

Barnaby c. reeves.

a Clinical Trials and Evaluation Unit, School of Clinical Sciences, University of Bristol, Level 7 Queen's Building, Bristol Royal Infirmary, Bristol BS2 8HW, UK

George A. Wells

b Department of Epidemiology and Community Medicine, Faculty of Medicine, University of Ottawa Heart Institute, 40 Ruskin Street, Ottawa, Ontario, Canada K1Y 4W7

Hugh Waddington

c International Initiative for Impact Evaluation (3ie), 202-203, Rectangle One, D-4, Saket District Centre, New Delhi, 110017, India

The aim of the study was to extend a previously published checklist of study design features to include study designs often used by health systems researchers and economists. Our intention is to help review authors in any field to set eligibility criteria for studies to include in a systematic review that relate directly to the intrinsic strength of the studies in inferring causality. We also seek to clarify key equivalences and differences in terminology used by different research communities.

Study Design and Setting

Expert consensus meeting.

The checklist comprises seven questions, each with a list of response items, addressing: clustering of an intervention as an aspect of allocation or due to the intrinsic nature of the delivery of the intervention; for whom, and when, outcome data are available; how the intervention effect was estimated; the principle underlying control for confounding; how groups were formed; the features of a study carried out after it was designed; and the variables measured before intervention.

The checklist clarifies the basis of credible quasi-experimental studies, reconciling different terminology used in different fields of investigation and facilitating communications across research communities. By applying the checklist, review authors' attention is also directed to the assumptions underpinning the methods for inferring causality.

What is new?

• • Evaluations of health system interventions have features that differ and which are described differently compared to evaluations of health care interventions.
• • An existing checklist of features has been extended to characterize: nesting of data in organizational clusters, for example, service providers; number of outcome measurements and whether outcomes were measured in the same or different individuals; whether the effects of an intervention are estimated by change over time or between groups; and the intrinsic ability of the analysis to control for confounding.
• • Evaluations of health care and health system interventions have features that affect their credibility with respect to establishing causality but which are not captured by study design labels.
• • With respect to inferring causality, review authors need to consider these features to discriminate “strong” from “weak” designs.
• • Review authors can define eligibility criteria for a systematic review with reference to these study design features, but applying the checklist does not obviate the need for a careful risk of bias assessment.

1. Introduction

There are difficulties in drawing up a taxonomy of study designs to evaluate health care interventions or systems that do not use randomization [1] . To avoid the ambiguities of study design labels, a checklist of design features has been proposed by the Cochrane Non-Randomized Studies Methods Group (including B.C.R. and G.A.W.) to classify nonrandomized studies of health care interventions on the basis of what researchers did [1] , [2] . The checklist includes items about: whether a study made a comparison and, if yes, how comparison groups were formed; the timing of key elements of a study in relation to its conduct; and variables compared between intervention and comparator groups [1] , [2] . The checklist was created primarily from the perspective of health care evaluation, that is, the kinds of intervention most commonly considered in Cochrane reviews of interventions.

The checklist works well in principle for study designs in which the allocation mechanism applies to individual participants, although it does not characterize unit of analysis issues that may arise from the mechanism of allocation or the organizational hierarchy through which an intervention is provided (clustering by practitioner or organizational unit on which allocation is based), unit of treatment issues arising from the organizational hierarchy through which the intervention is provided, or unit of analysis issues arising from the unit at which data are collected and analysed (whether patient, practitioner or organisational aggregate). Most health interventions are delivered by discrete care provider units, typically organized hierarchically (e.g., hospitals, family practices, practitioners); this makes clustering important, except when allocation is randomized, because interventions are chosen by care provider units in complex ways. A modified checklist was also suggested for cluster-allocated designs (diverse study designs in which the allocation mechanism applies to groups of participants) [1] , [2] , often used to evaluate interventions applied at the level of the group (e.g., disease prevention, health education, health policy), but the authors acknowledged that this checklist had not been well piloted.

There are three key challenges when trying to communicate study designs that do not use randomization to evaluate the effectiveness of interventions. First, study design labels are diverse or ambiguous, especially for cluster-allocated designs; moreover, there are key differences between research fields in the way that similar designs are conceived. Second, some study designs are, in fact, strategies for analysis rather than designs per se. Terms such as quasi-experimental, natural experiment, and observational cause particular ambiguity. The current checklist does not explicitly consider designs/analyses commonly used in health systems research (including so-called “credible quasi-experimental studies” [3] , [4] ), often taking advantage of large administrative or other available data sets, and in other cases using data purposely collected as part of prospective designs where random assignment is not feasible. Third, and important with respect to the motivation for this paper, differences of opinion exist between health care and health systems researchers about the extent to which some studies are “as good as” randomized trials when well conducted; it is not clear whether this is because common designs are described with different labels or whether there are substantive differences. Therefore, our primary aim in this paper is revise the checklist to overcome these limitations.

Specific objectives were (1) to include a question to capture information about clustering; and (2) to extend the checklist to include study designs often used by health systems researchers and econometricians in a way that deals with the design/analysis challenge. We intended that the revised checklist should be able to resolve the differences in opinion about the extent to causality can be inferred from nonrandomized studies with different design features, improving communication between different health research communities. We did not intend that the checklist should be used as a tool to assess risk of bias, which can vary across studies with the same design features.

The paper is structured in three parts. Part 1 sets out designs currently used for health systems evaluations, illustrating their use through inclusion of different designs/analyses in a recent systematic review. Part 2 describes designs used for health intervention/program evaluations. Part 3 clarifies some of the ambiguities of study design labels using the proposed design feature framework.

2. Part 1: “quasi-experimental” studies considered by health system researchers and health economists

Health systems researchers and health economists use a wide range of “quasi-experimental” approaches to estimate causal effects of health care interventions. Some methods are considered stronger than others in estimating an unbiased causal relationship. “Credible quasi-experimental studies” are ones that “estimate a causal relationship using exogenous variation in the exposure of interest which is not usually directly controlled the researcher.” This exogenous variation refers to variation determined outside the system of relationships that are of interest and in some situations may be considered “as good as random” variation [3] , [4] , [5] . Credible quasi-experimental approaches are based on assignment to treatment and control that is not controlled by the investigators, and the term can be applied to different assignment rules; allocation to treatment and control is by definition not randomized, although some are based on identifying a source of variation in an exposure of interest that is assumed to be random (or exogenous). In the present context, they are considered to use rigorous designs and methods of analysis which can enable studies to adjust for unobservable sources of confounding [6] and are identical to the union of “strong” and “weak” quasi-experiments as defined by Rockers et al. [4] .

Credible quasi-experimental methods use assignment rules which are either known or can be modeled statistically, including: methods based on a threshold on a continuous scale (or ordinal scale with a minimum number of units) such as a test score (regression discontinuity design) or another form of “exogenous variation” arising, for example, due to geographical or administrative boundaries or assignment rules that have gone wrong (natural experiments). Quasi-experimental methods are also applied when assignment is self-selected by program administrators or by beneficiaries themselves [7] , [8] . Credible methods commonly used to identify causation among self-selected groups include instrumental variable estimation (IVE), difference studies [including difference in differences, (DIDs)] and, to a lesser extent, propensity score matching (PSM) where individuals or groups are matched on preexisting characteristics measured at baseline and interrupted time series (ITS). Thumbnail sketches of these and other designs used by health system researchers are described in Box 1 . It should be noted that the sketches of study types used by health program evaluators are not exhaustive. For example, pipeline studies, where treatment is withheld temporarily in one group until outcomes are measured (where time of treatment is not randomly allocated), are also used.

Thumbnail sketches of quasi-experimental studies used in program evaluations of CCT programs

Quasi-experimental methods are used increasingly to evaluate programs in health systems research. Gaarder et al. [11] , Baird et al. [12] , and Kabeer and Waddington [13] have published reviews incorporating quasi-experimental studies on conditional cash transfer (CCT) programs, which make welfare benefits conditional upon beneficiaries taking specified actions like attending a health facility during the pre/post-natal period or enrolling children in school. Other reviews including quasi-experimental studies have evaluated health insurance schemes [14] , [15] and maternal and child health programs [16] . Other papers in this themed issue of the Journal of Clinical Epidemiology describe how quasi-experimental studies can be identified for evidence synthesis [17] , how data are best collected from quasi-experimental studies [18] , and how the global capacity for including quasi-experimental studies in evidence synthesis can best be expanded [19] , [20] . In this paper, we use studies from the reviews on the effects of CCT programs to illustrate the wide range of quasi-experimental methods used to quantify causal effects of the programs ( Table 1 ).

Table 1

Experimental and quasi-experimental approaches applied in studies evaluating the effects of conditional cash transfer (CCT) programs

Some of the earliest CCT programs randomly assigned clusters (communities of households) and used longitudinal household survey data collected by researchers to estimate the effects of CCTs on the health of both adults and children [21] . The design and analysis of a cluster-randomized controlled trial of this kind is familiar to health care researchers [29] .

In other cases, it was not possible to assign beneficiaries randomly. In Jamaica's PATH program [22] , benefits were allocated to people with scores below a criterion level on a multidimensional deprivation index and the effects of the program were estimated using a regression discontinuity analysis. This study involved recruiting a cohort of participants being considered for benefits, to whom a policy decision was applied (i.e., assign benefits or not on the basis the specified deprivation threshold). In such studies, by assigning the intervention on the basis of a cutoff value for a covariate, the assignment mechanism (usually correlated with the outcome of interest) is completely known and can provide a strong basis for inferences, although usually in a less efficient manner than in randomized controlled trials (RCTs). The treatment effect is estimated as the difference (“discontinuity”) between two predictions of the outcome based on the covariate (the average treatment effect at the cutoff): one for individuals just above the covariate cutoff (control group) and one for individuals just below the cutoff (intervention group) [30] . The covariate is often a test score (e.g., to decide who receives a health or education intervention) [31] but can also be distance from a geographic boundary [32] . Challenges of this design are assignment determined approximately, but not perfectly, by the cutoff [33] or circumstances in which participants may be able to control factors determining their assignment status such as their score or location.

As with health care evaluation, many studies in health systems research combine multiple methods. In Ecuador's Bono de Desarrollo Humano program, leakages in implementation caused ineligible families to receive the program, compromising the original discontinuity assignment. To compensate for this problem, the effects of the program were estimated as a “fuzzy discontinuity” using IVE [23] . An instrument (in this case, a dichotomous variable taking the value of 1 or 0 depending on whether the participating family had a value on a proxy means test below or above a cutoff value used to determine eligibility to the program) must be associated with the assignment of interest, unrelated to potential confounding factors and related to the outcome of interest only by virtue of the relationship with the assignment of interest (and not, e.g., eligibility to another program which may affect the outcome of interest). If these conditions hold, then an unbiased effect of assignment can be estimated using two-stage regression methods [10] . The challenge lies not in the analysis itself (although such analyses are, typically, inefficient) but in demonstrating that the conditions for having a good instrument are met.

In the case of Bolsa Alimentação in Brazil, a computer error led eligible participants whose names contained nonstandard alphabetical characters to be excluded from the program. Because there are no reasons to believe that these individuals would have had systematically different characteristics to others, the exclusion of individuals was considered “as good as random” (i.e., a true natural experiment based on quasi-random assignment) [9] .

Comparatively few studies in this review used ITS estimation, and we are not aware of any studies in this literature which have been able to draw on sufficiently long time series with longitudinal data for individual units of observation in order for the design to qualify “as good as randomized.” An evaluation of Nepal's Safe Delivery Incentive Programme (SDIP) drew on multiple cohorts of eligible households before and after implementation over a 7-year period [24] . The outcome (neonatal mortality) for each household was available at points in time that could be related to the inception of the program. Unfortunately, comparison group data were not available for nonparticipants, so an analysis of secular trends due to general improvements in maternal and child health care (i.e., not due to SDIP) was not possible. However, the authors were able to implement a regression “placebo test” (sometimes called a “negative control”), in which SDIP treatment was linked to an outcome (use of antenatal care) which was not expected to be affected by the program, the rationale being that the lack of an estimated spike in antenatal care at the time of the expected change in mortality might suggest that these other confounding factors were not at play. But ultimately, due to the lack of comparison group data, the authors themselves note that the study is only able to provide “plausible evidence of an impact” rather than probabilistic evidence (p. 224).

Individual-level DID analyses use participant-level panel data (i.e., information collected in a consistent manner over time for a defined cohort of individuals). The Familias en Accion program in Colombia was evaluated using a DID analysis, where eligible and ineligible administrative clusters were matched initially using propensity scores. The effect of the intervention was estimated as the difference between groups of clusters that were or were not eligible for the intervention, taking into account the propensity scores on which they were matched [25] . DID analysis is only a credible method when we expect unobservable factors which determine outcomes to affect both groups equally over time (the “common trends” assumption). In the absence of common trends across groups, it is not possible to attribute the growth in the outcome to the program using the DID analysis. The problem is that we rarely have multiple period baseline data to compare variation between groups in outcomes over time before implementation, so the assumption is not usually verifiable. In such cases, placebo tests on outcomes which are related to possible confounders, but not the program of interest, can be investigated (see also above). Where multiple period baseline data are available, it may be possible to test for common trends directly and, where common trends in outcome levels are not supported, undertake a “difference-in-difference-in-differences” (DDDs) analysis. In Cambodia, the evaluators used DDD analysis to evaluate the Cambodia Education Sector Support Project, overcoming the observed lack of common trends in preprogram outcomes between beneficiaries and nonbeneficiaries [26] .

As in the case of Attanasio et al. above [25] , difference studies are usually made more credible when combined with methods of statistical matching because such studies are restricted to (or weighted by) individuals and groups with similar probabilities of participation based on observed characteristics—that is, observations “in the region of common support.” However, where panel or multiple time series cohort data are not available, statistical matching methods are often used alone. By contrast with the above examples, a conventional cohort study design was used to evaluate Tekoporã in Paraguay, relying on PSM and propensity weighted regression analysis of beneficiaries and nonbeneficiaries at entry into the cohort to control for confounding [27] . Similarly, for Bolsa Familia in Brazil evaluators applied PSM to cross-sectional (census) data [28] . Variables used to match observations in treatment and comparison should not be determined by program participation and are therefore best collected at baseline. However, this type of analysis alone does not satisfy the criterion of enabling adjustment for unobservable sources of confounding because it cannot rule out confounding of health outcomes data by unmeasured confounding factors, even when participants are well characterized at baseline.

3. Part 2: “quasi-experimental” designs used by health care evaluation researchers

The term “quasi-experimental” is also used by health care evaluation and social science researchers to describe studies in which assignment is nonrandom and influenced by the researchers. At the first appearance, many of the designs seem similar, although they are often labeled differently. Although an assignment rule may be known, it may not be exploitable in the way described above for health system evaluations; for example, quasi-random allocation may be biased because of a lack of concealment, even when the allocation rule is “as good as random.”

Researchers also use more conventional epidemiological designs, sometimes called observational, that exploit naturally occurring variation. Sometimes, the effects of interventions can be estimated in these cohorts using instrumental variables (prescribing preference; surgical volume; geographic variation, distance from health care facility), quantifying the effects of an intervention in a way that is considered to be unbiased [34] , [35] , [36] . Instrumental variable estimation using data from a randomized controlled trial to estimate the effect of treatment in the treated, when there is substantial nonadherence to the allocated intervention, is a particular instance of this approach [37] , [38] .

Nonrandomized study design labels commonly used by health care evaluation researchers include: nonrandomized controlled trial, controlled before-and-after study (CBA), interrupted time series study (ITS; and CITS), prospective, retrospective or historically controlled cohort studies (PCS, RCS and HCS respectively), nested case–control study, case–control study, cross-sectional study, and before-after study. Thumbnail sketches of these study designs are given in Box 2 . In addition, researchers sometimes report findings for uncontrolled cohorts or individuals (“case” series or reports), which only describe outcomes after an intervention [54] ; these are not considered further because these studies do not collect data for an explicit comparator. It should be noted that these sketches are the authors' interpretations of the labels; studies that other researchers describe using these labels may not conform to these descriptions.

Thumbnail sketches of quasi-experimental study designs used by health care evaluation researchers

The designs can have diverse features, despite having the same label. Particular features are often chosen to address the logistical challenges of evaluating particular research questions and settings. Therefore, it is not possible to illustrate them with examples drawn from a single review as in part 1; instead, studies exemplifying each design are cited across a wide range of research questions and settings. The converse also occurs, that is, study design labels are often inconsistently applied. This can present great difficulties when trying to classify studies, for example, to describe eligibility for inclusion in a review. Relying on the study design labels used by primary researchers themselves to describe their studies can lead to serious misclassifications.

For some generic study designs, there are distinct study types. For example, a cohort study can study intervention and comparator groups concurrently, with information about the intervention and comparator collected prospectively (PCS) or retrospectively (RCS), or study one group retrospectively and the other group prospectively (HCS). These different kinds of cohort study are conventionally distinguished according to the time when intervention and comparator groups are formed, in relation to the conception of the study. Some studies are sometimes incorrectly termed PCS, in our view, when data are collected prospectively, for example, for a clinical database, but when definitions of intervention and comparator required for the evaluation are applied retrospectively; in our view, this should be an RCS.

4. Part 3: study design features and their role in disambiguating study design labels

Some of the study designs described in parts 1 and 2 may seem similar, for example, DID and CBA, although they are labeled differently. Some other study design labels, for example, CITS/ITS, are used in both types of literature. In our view, these labels obscure some of the detailed features of the study designs that affect the robustness of causal attribution. Therefore, we have extended the checklist of features to highlight these differences. Where researchers use the same label to describe studies with subtly different features, we do not intend to imply that one or other use is incorrect; we merely wish to point out that studies referred to by the same labels may differ in ways that affect the robustness of an inference about the causal effect of the intervention of interest.

The checklist now includes seven questions ( Table 2 ). The table also sets out our responses for the range of study designs as described in Box 1 , Box 2 . The response “possibly” (P) is prevalent in the table, even given the descriptions in these boxes. We regard this as evidence of the ambiguity/inadequate specificity of the study design labels.

Table 2

Quasi-experimental taxonomy features checklist

Abbreviations: RCT, randomized controlled trial; Q-RCT, quasi-randomized controlled trial; IV, instrumental variable; RD, regression discontinuity; CITS, controlled interrupted time series; ITS, interrupted time series; DID, difference-in-difference; CBA, controlled before-and-after study; NRCT, nonrandomized controlled trial; PCS, prospective cohort study; RCS, retrospective cohort study; HCT, historically controlled study; NCC, nested case–control study; CC, case–control study; XS, cross-sectional study; BA, before-after study; Y, yes; N, no; P, possibly; na, not applicable.

Cells in the table are completed with respect to the thumbnail sketches of the corresponding designs described in Box 1 , Box 2 .

Question 1 is new and addresses the issue of clustering, either by design or through the organizational structure responsible for delivering the intervention ( Box 3 ). This question avoids the need for separate checklists for designs based on assigning individual and clusters. A “yes” response can be given to more than one response item; the different types clustering may both occur in a single study and implicit clustering can occur an individually allocated nonrandomized study.

Clustering in studies evaluating the effects of health system or health care interventions

Clustering is a potentially important consideration in both RCTs and nonrandomized studies. Clusters exist when observations are nested within higher level organizational units or structures for implementing an intervention or data collected; typically, observations within clusters will be more similar with respect to outcomes of interest than observations between clusters. Clustering is a natural consequence of many methods of nonrandomized assignment/designation because of the way in which many interventions are implemented. Analyses of clustered data that do not take clustering into account will tend to overestimate the precision of effect estimates.

Clustering occurs when implementation of an intervention is explicitly at the level of a cluster/organizational unit (as in a cluster-randomized controlled trial, in which each cluster is explicitly allocated to control or intervention). Clustering can also arise implicitly, from naturally occurring hierarchies in the data set being analyzed, that reflect clusters that are intrinsically involved in the delivery of the intervention or comparator. Both explicit and implicit clustering can be present in a single study.

Examples of types of cluster

• • Practitioner (surgeon; therapist, family doctor; teacher; social worker; probation officer; etc.).
• • Organizational unit [general practice, hospital (ward), community care team; school, etc.].
• • Social unit (family unit; network of individuals clustered in some nongeographic network, etc.).
• • Geographic area (health region; city jurisdiction; small electoral district, etc.).

“Explicit” clustering

• • Clustering arising from allocation/formation of groups; clusters can contain only intervention or control observations.

“Implicit” clustering

• • Clustering arising from naturally occurring hierarchies of units of analysis in the data set being analyzed to answer the research question.
• • Clusters can contain intervention and control observations in varying proportions.
• • Factors associated with designation as intervention or control may vary by cluster.

No clustering

• • Designation of an observation as intervention or control is only influenced by the characteristics of the observation (e.g., patient choice to self-medicate with an over-the-counter medication; natural experiment in which allocation of individuals is effectively random, as in the case of Bolsa Alimentação where a computer error led to the allocation to intervention or comparator [31] .)

Question 1 in the checklist distinguishes individual allocation, cluster allocation (explicit clustering), and clustering due to the organizational hierarchy involved in the delivery of the interventions being compared (implicit clustering). Users should respond factually, that is, with respect to the presence of clustering, without making a judgment about the likely importance of clustering (degree of dependence between observations within clusters).

Questions 2–4 are also new, replacing the first question (“Was there a relevant comparison?”) in the original checklist [1] , [2] . These questions are designed to tease apart the nature of the research question and the basis for inferring causality.

Question 2 classifies studies according to the number of times outcome assessments were available. In each case, the response items distinguish whether or not the outcome is assessed in the same or different individuals at different times. Only one response item can be answered “yes.”

Treatment effects can be estimated as changes over time or between groups. Question 3 aims to classify studies according to the parameter being estimated. Response items distinguish changes over time for the same or different individuals. Only one response item can be answered “yes.”

Question 4 asks about the principle through which the primary researchers aimed to control for confounding. Three response items distinguish methods that:

• a. control in principle for any confounding in the design, that is, by randomization, IVE, or regression discontinuity;
• b. control in principle for time invariant unobserved confounding, that is, by comparing differences in outcome from baseline to end of study, using longitudinal/panel data for a constant cohort; or
• c. control for confounding only by known and observed covariates (either by estimating treatment effects in “adjusted” statistical analyses or in the study design by restricting enrollment, matching and/or stratified sampling on known, and observed covariates).

The choice between these items (again, only one can be answered “yes”) is key to understanding the basis for inferring causality.

Questions 5–7 are essentially the same as in the original checklist [1] , [2] . Question 5 asks about how groups (of individuals or clusters) were formed because treatment effects are most frequently estimated from between group comparisons. An additional response option, namely by a forcing variable, has been included to identify credible quasi-experimental studies that use an explicit rule for assignment based on a threshold for a variable measured on a continuous or ordinal scale or in relation to a spatial boundary. When answering “yes” to this item, the review author should also identify the nature of the variable by answering “yes” to another item. Possible assignment rules are identified: the action of researchers, time differences, location differences, health care decision makers/practitioners, policy makers, on the basis of the outcome, or some other process. Other, nonexperimental, study designs should be classified by the method of assignment (same list of variables) but without there being an explicit assignment rule.

Question 6 asks about important features of a study in relation to the timing of their implementation. Studies are classified according to whether three key steps were carried out after the study was designed, namely: acquisition of source data to characterize individuals/clusters before intervention; actions or choices leading to an individual or cluster becoming a member of a group; and the assessment of outcomes. One or more of these items can be answered “yes,” as would be the case for all steps in a conventional RCT.

Question 7 asks about the variables that were measured and available to control for confounding in the analysis. The two broad classes of variables that are important are the identification and collection of potential confounder variables and baseline assessment of the outcome variable(s). The answers to this question will be less important if the researchers of the original study used a method to control for any confounding, that is, used a credible quasi-experimental design.

The health care evaluation community has historically been much more difficult to win around to the potential value of nonrandomized studies to evaluate interventions. We think that the checklist helps to explain why, that is, because designs used in health care evaluation do not often control for unobservables when the study features are examined carefully. To the extent that these features are immutable, the skepticism is justified. However, to the extent that studies may be possible with features that promote the credibility of causal inference, health care evaluation researchers may be missing an opportunity to provide high-quality evidence.

Reflecting on the circumstances of nonrandomized evaluations of health care and health system interventions may provide some insights why these different groups have disagreed about the credibility of effects estimated in quasi-experimental studies. The checklist shows that credible quasi-experimental studies gain credibility from using high-quality longitudinal/panel data; such data characterizing health care are rare, leading to evaluations that “make do” with the data that are available in existing information systems.

The risk of confounding in health care settings is inherently greater because participants' characteristics are fundamental to choices about interventions in usual care; mitigating against this risk requires high-quality clinical data to characterize participants at baseline and, for pharmaco-epidemiological studies about safety, often over time. Important questions about health care for which quasi-experimental methods of evaluation are typically considered are often to do with the outcome of discrete episodes of care, usually binary, rather than long-term outcomes for a cohort of individuals; this can lead to a focus on the invariant nature of the organizations providing the care rather than the varying nature of the individuals receiving care. These contrasts are apparent between, for example: DID studies using panel data to evaluate an intervention such as CCT among individuals with CBA studies of an intervention implemented at an organizational level studying multiple cross-sections of health care episodes; or credible and less credible interrupted time series.

There is a new article in the field of hospital epidemiology which also highlights various features of what it terms as quasi-experimental designs [56] . The list of features appears to be aimed at researchers designing a quasi-experimental study, acting more as a prompt (e.g., “consider options for …”) rather than as a checklist for a researcher appraising a study to communicate clearly to others about the nature of a published study, which is our perspective (e.g., a review author). There is some overlap with our checklist, but the list described also includes several study attributes intended to reduce the risk of bias, for example, blinding. By contrast, we consider that an assessment of the risk of bias in a study is essential and needs to be carried out as a separate task.

5. Conclusion

The primary intention of the checklist is to help review authors to set eligibility criteria for studies to include in a review that relate directly to the intrinsic strength of the studies in inferring causality. The checklist should also illuminate the debate between researchers in different fields about the strength of studies with different features—a debate which has to date been somewhat obscured by the use of different terminology by researchers working in different fields of investigation. Furthermore, where disagreements persist, the checklist should allow researchers to inspect the basis for these differences, for example, the principle through which researchers aimed to control for confounding and shift their attention to clarifying the basis for their respective responses for particular items.

Acknowledgments

Authors' contributions: All three authors collaborated to draw up the extended checklist. G.A.W. prepared the first draft of the paper. H.W. contributed text for Part 1. B.C.R. revised the first draft and created the current structure. All three authors approved submission of the final manuscript.

Funding: B.C.R is supported in part by the U.K. National Institute for Health Research Bristol Cardiovascular Biomedical Research Unit. H.W. is supported by 3ie.

Motion planning method and experimental research of medical moxibustion robot of double manipulator arms

• Technical Paper
• Published: 22 August 2024
• Volume 46 , article number  564 , ( 2024 )

Cite this article

• Zhengyao Yi 1 ,
• Haoming Li 1 ,
• Jiasheng Zhu   ORCID: orcid.org/0009-0001-1657-8793 1 ,
• Bingxing Feng 1 ,
• Jie Cao 1 ,
• Xianshu Lu 2 &
• Baocheng Wang 3  

In order to alleviate the contradiction between the increasing demand of seafarers for moxibustion physiotherapy and the shortage of moxibustion doctors, a medical double-arm moxibustion robot was designed by using a six-degree-of-freedom mechanical arm and a four-degree-of-freedom mechanical arm to simulate traditional Chinese medicine moxibustion techniques. The robot coordinate system was established by D-H parameter method, and the forward and inverse kinematics of the robot model were calculated. The robot model was established and simulated by Robotics Toolbox in MATLAB. The angular velocity and angular acceleration curves of each joint and the trajectory and displacement of the robot end were obtained, and the feasibility of robot trajectory planning was verified. Through the preliminary design, the collaborative process of task assignment for double moxibustion robot was established. The simulation test bench was built to further simulate the temperature of human epidermis, and the relationship between the end distance of moxibustion robot and the heating of human epidermis was determined. The simulation and experimental results show that: a) The robot does not appear serious impact or stutter phenomenon in the simulation process, and the kinematics performance is good, which verifies the feasibility of the robot model; and b) during the simulation test, the heating temperature of human epidermis can be maintained at 43 °C, which realizes the expected moxibustion temperature of patients and verifies the effectiveness of the robot model.

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Ministry of Transport of the People's Republic of China. 2020 China Crew Development Report. [2021–06–25]. https://zs.mot.gov.cn/mot/s

Jinlu S (2010) Simulation analysis of seafarers’ seaworthiness in small organization environment. Chinese Journal of Safety Science 20(08):44–48

Google Scholar  

Tao Yu, Xiao W, Xiaopu Z, Aimin Z, Yong J, Jinhan Mo (2018) Distribution characteristics of BTEX in ship cabin environment and health risk assessment of crew exposure[C]//. Academic Conference on Environment and Health-Precise Environmental Health : Challenges for Interdisciplinary CooperationThesis Series 2018:432–433

Li Xiaopeng presided over the meeting and emphasized: optimizing the crew development environment to promote the construction of high-quality crew team.Transportation enterprise management, 2021, 36(02): 27.

Yan Caiju, Gu Yan. Clinical observation of moxibustion therapy combined with Gua Sha in the treatment of chronic pelvic inflammatory disease of cold-damp stagnation type. Frontier of international medical research, 2022, 6(2).

Kim JI, Choi JY, Lee H, Lee MS, Ernst E (2010) Moxibustion for hypertension: A systematic review. BMC Cardiovasc Disord 10(1):33

Article   Google Scholar  

Yin Shao, Zhu Fengya, Li Zhao, Che Deya, Li Liuying,Feng Jie, Zhang Lu, Huo Zhenyi. An Overview of Systematic Reviews of Moxibustion for Knee Osteoarthritis. Frontiers in Physiology, 2022, 13.

Ziqiang Ni, Tianmiao W, Da L (2015) An overview of the development of medical robotics. Journal of Mechanical Engineering 51(13):45–52

Zhang Jingxin Lu, Dongdong LQ, Wang Xuejun Lu, Mengye ZX, Yang Xiaoyuan Gu, Jiyu SY, Tiancheng Xu (2018) Research progress and key technology analysis of intelligent acupuncture robot. China Digital Medicine 13(10):2–4

Deng J, Yin C, Chen M, Tingbiao Wu, Zhang R, Zhang J (2019) Design and use of a moxibustion glasses holder. Chinese Acupuncture 39(10):1137–1140

Gao Ling, Wang Dongbin, Liu Huirong.Development and characteristics of multi-acupoint moxibustion apparatus.Chinese Acupuncture, 2018, 38(9): 1013–1015.

Li Min, Sun Zhiling. Development and characteristics of a fully automatic temperature-controlled moxibustion box.Chinese Acupuncture, 2019, 39(6): 649–650.

Wei W, Mei L, Ligong W (2012) Application and Significance of Multifunctional Moxibustion Treatment Bed. Chinese Acupuncture 32(7):665–667

Dai Yaonan, Chen Xubing. Design and implementation of thermostatic moxibustion robot for human back spine.Computer engineering and application, 2019, 55(9): 216–222.

Zhao Guoyou, Liu Yicheng, Tu Haiyan, Zhang Hanrui, Xia Shilin, Li Yingkun.Design and application of moxibustion manipulator.Acupuncture research, 2020, 45(11): 5.

Xia S, Tian S, Zhang H, Li Y, Haiyan Tu, Zhao G (2021) A design and application of moxibustion apparatus for multi-joint moxibustion manipulator. Chinese Acupuncture and Moxibustion 41(2):4

Yong Y, Lei M, Jiaqi X, Xiangyu Ye, Yang Z, Huayuan Y (2020) Design and implementation of an intelligent moxibustion manipulation simulation system. Beijing Biomed Eng 39(6):7

Yuhao Jin, Rong Yi, Jiangqiong Meng, Qiming Yang, Taipin Guo, Zeyi Li, Ruonan Li, Xiaoling Bai. Design and application of an automatic temperature-controlled moxibustion instrument.Acupuncture Clinical, 2018,34 (11) : 70–72.

Denavit J, Hartenberg RS (1995) A kinematic notation for lowerpair mechanisms based on matrices. J Appl Mech 22:215–221

Qazani M, Pedrammehr S, Rahmani A, Danaei B, Ettefagh MM, Rajab AKS, Abdi H (2015) Kinematic analysis and workspace determination of hexarot-a novel 6-DOF parallel manipulator with a rotation-symmetric arm system. Robotica 33(8):1686–1703

Zixing C (2009) Robotics, 2nd edn. Tsinghua University Press, Beijing

LIAO S, LI J. Kinematic simulation and analysis of robot based on MATLAB[C]/ /American Institute of Physics Conference Series, 2018: 020066–1–020066–5.

Cheng Kai, Liu Bo. Experimental observation on the effect of moxibustion at different temperatures on local skin burns.Clinical Medical Literature Electronic Journal, 2020,7 (30) : 57.

Xin Xu, Bin D, Qi W, Peiheng He, Ningbo L (2020) The skin temperature control system of moxibustion point based on self-tuning fuzzy PID. Electronic measurement technology 43(22):39–44

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This work was supported by the Dalian Science and Technology Innovation Fund (Grant No. 2021JJ13SN50) and Dalian Shield Safe Technology Ltd. (Grant No. 2020067).

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Yi, Z., Li, H., Zhu, J. et al. Motion planning method and experimental research of medical moxibustion robot of double manipulator arms. J Braz. Soc. Mech. Sci. Eng. 46 , 564 (2024). https://doi.org/10.1007/s40430-024-05139-8

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Nonlinear static and dynamic response of a metastructure exhibiting quasi-zero-stiffness characteristics for vibration control: an experimental validation

• Srajan Dalela   ORCID: orcid.org/0000-0002-5602-5253 1 ,
• P. S. Balaji   ORCID: orcid.org/0000-0002-6364-4466 1 ,
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This work introduces a novel metastructure designed for quasi-zero-stiffness (QZS) properties based on the High Static and Low Dynamic Stiffness mechanism. The metastructure consists of four-unit cells arranged in parallel, each incorporating inclined beams and semicircular arches. Under vertical compression, the inclined beams exhibit buckling and snap-through behavior, contributing negative stiffness, while the semicircular arches provide positive stiffness through bending-dominated behavior. The design procedure to achieve QZS is established and validated through finite element analysis and experimental investigations. The static analysis confirms a QZS region for specific displacement. Dynamic behavior is analyzed using a nonlinear dynamic equation solved using the Harmonic Balance Method, validated experimentally with transmissibility curves showing sudden jump down with effective vibration isolation. Parametric studies with varied payload masses and excitation amplitudes further verify the ability to of metastructure to attenuate vibrations effectively in low-frequency ranges.

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Introduction.

Mechanical vibration is widely present in engineering structures, which deteriorates the performance of machinery 1 , 2 , 3 , reduces the service life of precision instruments 4 , impacts human health 5 , and more. Therefore, it is crucial to protect the host structures from undesirable vibrations. Traditionally, linear passive vibration isolators can control vibrations in high and low-frequency ranges beyond \(\sqrt{2}\) times the natural frequency of the system. However, isolating vibrations in low-frequency ranges has been a significant challenge for researchers, as achieving a low natural frequency requires either low stiffness or high mass. To enhance isolation performance at low frequencies, nonlinear methods using nonlinear stiffness 6 , 7 , 8 and damping characteristics 9 , 10 , 11 have been adopted. Fortunately, quasi-zero-stiffness (QZS) mechanism-based nonlinear passive isolators substantially neutralize the shortcomings of linear isolators by designing systems that operate efficiently in low-frequency ranges without compromising load-bearing capacity 12 , 13 , 14 .

The QZS system operates on the High Static and Low Dynamic Stiffness (HSLDS) mechanism, implying that a system can be designed for high load-bearing capacity with a low-natural frequency for targeted loading 15 . Generally, a QZS isolator includes a combination of positive and negative stiffness structures. The element with high positive stiffness values incorporates small static deflection, while the element with negative stiffness neutralizes the total stiffness value in a certain displacement range. This arrangement helps to reduce dynamic stiffness and enhance vibration isolation characteristics. Various techniques have been utilized to achieve negative stiffness characteristics, including combinations of two structures or individual structures. Researchers have realized negative stiffness mechanisms (NSM) using elastic buckled beams 16 , 17 , 18 , 19 , oblique springs 20 , 21 , 22 , 23 , 24 , 25 , 26 , magnetic springs 27 , 28 , 29 , 30 , 31 , cam-roller mechanisms 32 , 33 , 34 , metamaterials 35 , 36 , 37 , 38 , 39 , disk springs 28 , 29 , 40 , bionic structures 11 , 41 , 42 , 43 , and pneumatic actuators 44 , 45 . However, most studies have used linear spring models to attain positive stiffness mechanisms (PSM). Additionally, the primary focus of researchers has been to develop various methods to achieve negative stiffness.

The initial configuration to achieve NSM is based on the arrangement of inclined springs. Carrella et al. 46 , 47 , 48 and Kovacic et al. 21 proposed and developed a QZS isolator using two oblique springs and one linear spring, further studying the static and dynamic characteristics of the isolator along with stability analysis. The dynamic analysis results suggest an excellent vibration isolation performance of the QZS isolator in low-frequency ranges compared to linear vibration isolators. Gatti 49 and Zhao et al. 26 used two pairs of oblique springs to increase the QZS region and studied the dynamic behavior of the developed model. To withstand large deformation and increase the QZS range, Liu and Yu 23 and Zhao et al. 24 used three pairs of oblique springs and experimentally studied the dynamic behavior for large amplitude vibrations. The use of oblique springs has the limitation of large geometrical size to achieve NSM, which is not beneficial for practical applications in high-weight-to-strength ratio 14 .

Different geometrical configurations were explored to achieve QZS behavior and widen the vibration isolation range in low-frequency ranges to overcome the mentioned limitation. Thanh et al. 50 proposed an isolator with two horizontal springs and two connecting rods to mitigate vibration reaching the driver seats. To increase the compactness of the isolator, Euler’s buckled beam was used as the negative stiffness corrector by 51 , 52 for the detuning of load and stiffness characteristics. Shaw et al. 53 proposed a QZS model with an adjustable configuration by placing the masses at different modal structures, which helps in adjusting the stiffness and symmetry of the device independently. Sun et al. 54 obtained QZS behavior using four horizontal springs acting as scissor-like structures and one vertical spring, Cheng et al. 55 designed a scissor-like structure to obtain nonlinear stiffness as well as damping and achieved improved isolation performance in the low-frequency range. Further, Lu et al. 56 performed a comparative study to analyze the effect of linear and nonlinear damping on the isolation performance. The results suggest better isolation in the low-frequency range with nonlinear damping.

Recently, QZS isolators have also been developed using magnetic springs and a cam-roller mechanism. Magnetic springs have certain advantages, such as there is no direct contact, so the effect of friction can be avoided, and electromagnets can also replace permanent magnets to add active control to the vibration isolator. Zhou et al. 57 used a pair of repelling magnets as a negative stiffness mechanism with a coil spring acting as a linear spring to achieve QZS behavior, whereas Zheng et al. 58 also used a similar arrangement to reduce the natural frequency of the QZS system and achieved improved vibration isolation in six directions. Different magnetic arrangements are used to achieve NSM for different applications, such as Wang et al. 59 used two magnetic rings to achieve a larger load range, Zhao et al. 60 designed a precision instrument for absolute displacement measurement using electromagnets as NSM, Yuan et al. 61 designed QZS with tunable electromagnetic ring for large working stroke.

Further, researchers also achieved QZS using a cam-roller mechanism and performed dynamic analysis to achieve isolation in low-frequency ranges 62 . One of the benefits of using a cam-roller mechanism is that the profile of the cam can be optimized, Li et al. 32 , 33 designed noncircular and user-defined based cam-profile, respectively, for achieving the QZS behavior and also achieved vibration isolation in varying frequency ranges. Lopez-Martinez et al. 63 designed three different cam profiles to achieve QZS using parabolic cams, springs, and rollers. Vibration isolation in torsional and translational directions simultaneously can also be achieved using the cam-roller structures 64 .

Inspired by the negative stiffness of origami metamaterials, Liu et al. 36 introduces a new quasi-zero stiffness (QZS) vibration isolation system with positive stiffness spring compensation, using the folding ratio as the principal coordinate to establish the static model and define the negative stiffness mechanism. In other work, Liu et al. 65 proposed an origami-inspired vibration isolator with QZS characteristics by integrating elastic joints based on the Tachi–Miura origami carton geometry to form a nonlinear stiffness model. Further, a truss-spring based stack Miura-ori (TS-SMO) structure is introduced to achieve QZS characteristics for the application as vibration isolation system 66 . Some of the works 67 , 68 also discussed the application of origami-inspired metamaterials to isolate the vibration in low-frequency region.

The bio-inspired QZS metastructure based isolators have also been developed to isolate the unwanted vibration disturbances in wide frequency ranges. Niu and Chen 69 and Zhao et al. 26 designed a compliant limb-like structure to induce nonlinearity in the system and obtained a quasi-zero stiffness region. Han et al. 70 proposed a NiTi-NOL circular ring-type single-element isolator by inducing stiffness and damping nonlinearities to obtain the QZS characteristics. Zhang et al. 71 used a topology optimization technique to design a single-element model for obtaining QZS characteristics. The same methodology is used by 72 to obtain a constant-force mechanism for vibration isolation. Some of the literature 38 , 73 discussed the mechanism of using compact structures to obtain QZS and further use it for vibration isolation applications.

To further enhance the width of the QZS region so that large amplitude excitations can get isolate in low-frequency regions, Liu et al. 74 proposed a higher-order stable QZS method composed of seven magnets and two linkages and experimentally obtained isolation region starting from 2.62 Hz for the 5th order QZS isolator. In other work 75 , a novel in-plane QZS vibration isolator composed of two magnetic rings that are radially magnetized and eight cables that are pre-tensioned is proposed for isolating horizontal vibration when the excitation is applied from two arbitrary direction in the horizontal plane. A review article discussed the ongoing application of electromagnetic mechanism for low-frequency nonlinear vibration isolation 76 . Kamaruzaman et al. 77 presents a comparison between passive and active stability analyses of a six degree of freedom QZS magnetic levitation vibration isolation system. By varying the lever arms, the passive rotational stability of the system is adjusted, and its effects on vibration isolation performance and control cost are investigated through static and dynamic simulations. More investigations have been performed to enhance the QZS properties for supporting multiple loads 78 , 79 , 80 , 81 . Moreover, recent article by Liu et al. 82 reviews the development of QZS vibration isolation technology, focusing on designs, improvements, and applications. It discusses construction approaches for QZS isolators, multi-degree-of-freedom systems, enhancement strategies, and engineering applications.

The QZS characteristics is based on the HSLDS mechanism, hence the isolators designed based on this property can isolate vibration for varying frequency ranges starting from lower frequency range to higher. Further, the QZS characteristics is material independent property as it depends on the deformation behavior of ductile materials, hence QZS based isolators possess wide range of applications in different industries such as-

Aerospace applications: To isolate vibrations in satellite payloads and precision instruments on aircraft.

Optical systems: To mitigate vibrations from reaching telescopes, and positioning of telescopic mounts.

Medical imaging devices: To provide stable environment for MRI machines to produce high-quality images, and in high-precision microscopes to ensure stable imaging.

Semiconductor manufacturing: To isolate sensitive equipment and maintain the necessary stability.

Precision instruments and laboratories: To maintain the stability required for accurate results.

Industrial machinery: Manufacturing of microelectronics assembly requires stable environment and accuracy.

As discussed, QZS isolators have applications focused mainly on the field of engines, vehicle seats, etc. However, the need for isolation in small precision instruments, microwave apparatus, binoculars, etc., is still in demand because of the size constraints. Meanwhile, to overcome this limitation, mechanical metamaterials can be used because of their peculiar properties, such as negative stiffness, high energy dissipations, bistable behavior, high damping ratio, and negative position ratio 83 . These properties can effectively help in mitigating wave propagation and help in reducing vibration at low-frequency ranges 13 . Auxetic metamaterial exhibiting negative Poisson’s ratio also helps in absorbing and dissipating the vibration energy, whereas origami material also helps in vibration isolation for broad bandwidth 38 . With the recent advancement in additive manufacturing processes, metamaterials can be designed and used for energy absorption. As the material properties of the metamaterials are material independent and depend majorly on the geometric configurations, the unit cell consisting of inclined beams and curve beams can be designed to achieve the snap-through or buckling behavior with a high strength-to-weight ratio, which is the main principle behind the shock absorptions 84 , 85 , 86 .

This work investigates a compact lightweight metastructure with high static and low dynamic stiffness. The metastructure is designed to exhibit stable QZS behavior to isolate vibration at low-frequency ranges, with the application majorly based on precision instruments. The structure is modeled using the inclined beam exhibiting negative stiffness and semicircular arch counteracting the negative stiffness to obtain the QZS behavior. Further, a dynamic study is performed to observe the nonlinear behavior along with stability analysis. In addition, samples are fabricated using a rapid-prototyping technique, and experiments are performed to validate the static and dynamic behavior. Here, the proof of concept is shown where the mass can be customized based on the frequency requirement by varying the geometrical parameters, which can tune the design as per the mass requirement of the practical application.

The paper is arranged in the following sequence, starting with the design of the prototype in section " Conceptual design of the prototype ", explaining the mechanism behind the structure and developing the analytical model. Further, the static characteristics are studied in section " Static characteristics " with analytical, numerical, and experimental studies. Based on the static study results, the dynamic performance is analyzed in section " Dynamic characteristics " by developing analytical model for frequency response and stability analysis and finally studying the vibration performance of the proposed metastructure experimentally.

Conceptual design of the prototype

The unit cell of the designed model, as depicted in Fig.  1 a, incorporates a combination of inclined beams and semicircular arches. These unit cells are subsequently aligned in parallel to construct the metastructure, as illustrated in Fig.  1 b. Upon placing a mass on the top plate of the metastructure, the inclined beam is subjected to buckling, resulting in negative stiffness, while the semicircular arch, through its bending-dominated behavior, contributes positive stiffness to balance the negative stiffness. A mass is positioned atop the metastructure and sinusoidal excitation is introduced at the bottom plate. This configuration allows the metastructure to serve as a platform for isolating unwanted vibrations from affecting the mass at the top.

( a ) Unit cell, ( b ) Metastructure.

Mechanism behind the structure

A bistable mechanism consisting of two beams of length \(L\) inclined at an angle \(\beta\) , is illustrated in Fig.  2 . These beams are symmetrically arranged, with one end of each beam fixed and the other end attached to a moving platform. When an external force \(P\) is exerted at the top of this platform, the inclined beams, along with the platform, experience a vertical displacement denoted by \(\delta\) . As the applied force increases, the inclined beam displays nonlinear behavior, transitioning through stable and unstable states, which are characterized by distinct mode shapes as illustrated in Fig.  3 . Initially, the beam remains in a stable state; however, with further increase in displacement, the beam undergoes snap-through to another stable state, also referred to as the bistable state. The period during which snap-through occurs corresponds to the unstable state, represented by dashed lines in Fig.  3 .

Deformation of the inclined beams under axially downward force. The dotted line represents the initial stable state of the system, and the solid red line represents the unstable state.

The buckling behavior of an inclined beam representing stable and unstable states.

The buckling behavior of the beams indicates that the structural energy within the beam comprises both bending and compression energy. As the beams begin to buckle, the bending energy increases continuously, whereas the compression energy rises to a peak at the centerline before it starts to decrease. The inclined beams are designed so that the reduction in compression energy surpasses the increase in bending energy due to the snap-through behavior; this results in a region of negative stiffness within the inclined beam 87 . The design of the proposed model is based on this mechanism, whereby the negative stiffness generated is balanced by the positive stiffness provided by the semicircular arch. Both the inclined beams and the semicircular arch must be carefully designed with specific parameters to achieve the desired quasi-zero-stiffness (QZS) behavior.

During the deformation of inclined beams, the axial force each beam exerts on the moving platform is equal and symmetric, ensuring the platform moves strictly downward in the axial direction. When the fixed end of a beam aligns with the guided end connected to the moving platform (depicted as a solid red line in Fig.  2 ), the system reaches an unstable equilibrium state. At this point, the external force is entirely supported by the in-plane lateral forces, with no axial force contributing, which triggers the snap-through of the beam to another stable state. The lateral forces exerted by each of the beams, \({P}_{1}\) and \({P}_{2}\) , are equal and opposite due to the symmetry of the mechanism. Consequently, the movement of the platform in the lateral direction is restricted; thus, only the axial component of the force is considered in the current study.

Under vertical loading, the semicircular arch primarily exhibits bending-dominated behavior, characterized by a linear positive stiffness region. The semicircular arches are designed specifically so that their positive stiffness effectively counteracts the negative stiffness demonstrated by the inclined beams. These beams and arches are organized into what is known as the unit cell, as depicted in Fig.  1 a. Additionally, these unit cells are aligned in parallel to construct the metastructure, as illustrated in Fig.  1 b.

Analytical modeling of the inclined beam and semicircular arch

The post-buckling behavior of the inclined beam is studied in this section. It is assumed that the deformation is bending-dominated, and the end of the beam deflects in the axial direction, whereas the length of the beam remains constant. Figure  4 shows an initially horizontal beam with length \(L\) being subjected to an end load \(\gamma F\) and an end moment \({M}_{0}\) . The end load can be divided into a horizontal force \(\lambda F\) and a vertical force \(F\) , \(\phi\) is the angle of end force with the \(x\) -axis, \({\theta }_{0}\) represents the deflected angle at the beam end, and \(\left(a,b\right)\) represents the coordinates of the beam at the guided end that is attached to the platform.

Deflected configuration of a beam under end-load \(\gamma F\) and moment \({M}_{0}\) .

In addition, it is assumed that the vertical force \(F\) is always positive and \({R}_{0}\) is introduced to denote the sign of the moment \({M}_{0}\) as,

Consider an arbitrary point \(A\) with coordinates \(\left(x,y\right)\) on the deflected beam. According to the Euler–Bernoulli beam theory, the moment \(M\) is given by:

where \(\frac{d\theta }{dr}\) is the curvature and \(EI\) is the flexural rigidity. From, Fig.  4 , \(M\) can also be given by,

Substituting Eq. ( 4 ) into Eq. ( 3 ), the curvature equation can be rewritten as:

In the above equations, the “ \(+\) ” sign signifies the concave curvature upwards, and the “−” sign signifies the concave curvature downwards. Detailed derivation can be seen in ref. 88

Equation ( 6 ) can be rearranged as,

\(k\) denotes the load ratio, \(\alpha\) is defined as the force index 88 :

Integrating Eq. ( 7 ) for the whole curvature,

Form Eq. ( 11 ), the force index \(\alpha\) can also be defined as,

For defining the movement at the tip of the beam, the expression for the coordinates \((a,b)\) needs to be defined. From Fig.  4 , it can be seen that:

Substituting Eq. ( 13 ) into Eq. ( 11 ) and integrating,

Substituting Eq. ( 10 ) into Eq. ( 14 ),

Equations ( 15 ) and ( 12 ) collectively represent the general formula for the post-buckling analysis of beams under large deformation conditions. Various approaches have been explored to solve large deformation problems, including finite element models 89 , elliptical integral models 90 , 91 , chained-beam constraint models 92 , and chain algorithms 93 . Among others, Ma and Chen 92 evaluated different methods for solving the bistable compliant mechanism in their study and implemented the chained-beam constraint model. On the other hand, Zhang and Chen 76 conducted an extensive study of the elliptical integral solution.

It can be observe that, the chained beam method clearly provides a more precise identification of the first mode of the inclined beam. Conversely, the elliptical integral solution offers a closed-loop solution that is more effective in analyzing the linear negative stiffness curve. Given that the inclined beam in this work exhibits a linear negative stiffness region, the elliptical integral solution method is employed to solve the derived general equation.

In the fixed-guided scenario, when a vertical force \({F}_{v}\) is applied to the platform, the beam undergoes bending, and the slope at the ends of the beams is constrained due to the motion being restricted in the axial direction, meaning that \({\theta }_{0}\approx 0\) . As the angle at both the fixed and guided ends remains constant, this configuration inevitably leads to the presence of at least one inflection point. Geneally, in cases involving large deformations, only one or two inflection points are considered. These inflection points correspond to different buckling mode shapes of the beam.

For the fixed-guided inclined beam mechanism, each inflection point marks a change in the curvature of the beam, signifying that the internal resisting moment vanishes at these points. Figure  5 a illustrates the fixed-guided case where \({\theta }_{0}\approx 0\) and \({F}_{v}\) denotes the applied vertical force at the guided end of the beam.

( a ) Represents the deflected and undeflected path of fixed-guided mechanism, and ( b ) represents the force and moment acting on the guided end of the beam.

Solving the derived Eqs. ( 12 ) and ( 15 ) using the elliptical integral solution and substituting the fixed-guided condition \({\theta }_{0}\approx 0\) 94 , we obtain:

in which \(\alpha , \gamma ,\lambda\) are the parameters already discussed earlier. \((a/L, b/L)\) denote the \((x, y)\) coordinates of the guided end tip, \({R}_{r}\) is be defined as:

where, \({R}_{r}\) denotes the sign of the moment of the fixed end \({M}_{r}\) , \({R}_{0}\) denotes the sign of the moment of the guided end \({M}_{0}\) , and \(m\) denotes the number of inflection points. The parameters \(f, e, c\) can be defined as:

where, \({\lambda }_{1}\) is the elliptic integral amplitude at the fixed end and \(t\) is the modulus, which can be expressed as:

And \(\eta\) is computed by substituting \({\theta }_{0}\approx 0\) in Eq. ( 8 ):

\(F(\gamma ,t)\) denotes the incomplete elliptical integral of the first kind and \(E(\gamma ,t)\) denotes the incomplete elliptical integral of the second kind, which can be given by 91 :

\(t\) represents the modulus \(\left(-1\le t\le 1\right)\) and \(\gamma\) represents the amplitude of elliptical integral. For \(\gamma =\pi /2\) , Eqs. ( 24 ) and ( 25 ) became complete integrals of the first and second kind and denoted as \(F\left(t\right)\) and E \(\left(t\right)\) . When the force is applied on the moving platform, the guided beam gets displaced by displacement \(\delta\) shown in Fig.  5 a, where \(\beta\) is the inclination angle of the beam. The coordinates \((a,b)\) can be computed as:

For the applied displacement \(\delta\) and the known inclination angle \(\beta\) , the value of guided end coordinates \((a,b)\) can be calculated from Eqs. ( 26 ) and ( 27 ). Substituting the known values of \(a\) and b into Eq. ( 17 ), the value of \(\lambda\) , \(\gamma\) (from Eq. ( 2 )) and \(c\) (from Eq. ( 21 )) can be calculated. Substituting the values of \(c\) , \(\lambda\) and \(\gamma\) into Eq. ( 17 ), a relation between \(f\) and \(e\) can be obtained, which is further used to find the value of \(t\) by performing a numerical iteration in Eqs. ( 19 ) and ( 20 ). Further, the obtained value of \(t\) is substituted into Eqs. ( 22 ) and ( 8 ) to calculate the value of \(\eta\) and \(k\) respectively 94 . Finally, the values of \(F\) and \({M}_{0}\) (depicted in Fig.  5 b) can be obtained using Eqs. ( 9 ), ( 10 ), and ( 16 ).

Based on the derived analytical model, the reaction force of the single inclined beam at the guided end can be expressed as :

Since the proposed model consists of two inclined beams to achieve symmetry and balance the in-plane lateral force, the total reaction force of the beam \({F}_{b}\) is then expressed as:

The buckling behavior of the fixed-guided inclined beam, as illustrated in Fig.  6 , can be observed through the developed model. Initially, the deformation exhibits the beam in its first mode shape characterized by a single inflection point (A). As the deformation increases, the beam transitions into the second mode shape, which includes two inflection points (B and C). The force–displacement characteristics of the inclined beam, along with the relevant design parameters, are further explored in section " Mechanical model of the structure ".

Buckling behavior of fixed-guided inclined beam depicting the obtained two mode shapes, where ( A–C ) represent the inflection points.

The vertical force acting on the semicircular arch leads to the bending of the arches. In this regard, the arch acts as a linear spring with constant positive stiffness as shown in Fig.  7 . The stiffness \({k}_{s}\) of a single arch is directly proportional to the elastic modulus \(E\) and second moment of inertia \({I}_{2}\) and inversely proportional to the cube of the length of the arch \({l}_{2}\) and it can be expressed as 95 :

Non-dimensional force–displacement curve of a single semi-circular arch.

Here, \(\nabla\) is a non-dimensional coefficient that depends on the cross-section of the arch. The numerical value of \(\nabla\) is determined according to the study by Fan et al. 96 . Fan et al. carried out a series of FEA analyses and plotted the non-dimensional stiffness versus the non-dimensional parameter \({t}_{2}/{l}_{2}\) ( \({t}_{2}\) is the thickness of semi-circular arch). Nonlinear regression analysis was then carried out to find that \(\nabla =18.257\) , and it is valid for the case of constant arch width. This relation is used in section " Mechanical model of the structure " to design the semi-circular arch.

Mechanical model of the structure

A unit cell in the structure is composed of inclined beams and semicircular arches, with their respective dimensions detailed in Fig.  8 . For the inclined beam, L represents the length, \(\beta\) denotes the inclination angle with the \(x\) -axis, \(I\) is the second moment of inertia of the cross-section, and \(t\) indicates the thickness. Regarding the semicircular arch, \({L}_{2}\) represents the length, \({t}_{2}\) is the thickness, \({I}_{2}\) denotes the moment of inertia of the cross-section, and \(R= {L}_{2}/4\) specifies the radius of the arch. Both the width and Young’s modulus are consistent across components and are denoted as \(b\) and \(E\) , respectively.

Represents the dimensions of the inclined beam and semicircular arch.

To evaluate the performance of the inclined beam, the parameters specific to it are defined and listed in Table 1 . By applying an initial deflection \(\delta\) to the moving platform, the inclined beam is subjected to deformation. From this deformation, the force \(F\) and the parameter \(\lambda\) can be determined using the analytical model developed in section " Analytical modeling of the inclined beam and semicircular arch ", based on the design parameters reported in Table 1 .

The values of force and various parameters obtained from the analytical solution are presented in Table 2 . Further, by substituting the obtained values of force \(F\) into Eq. ( 29 ), the total reaction force of the beam \({F}_{b}= 2{F}_{v}\) is calculated and plotted against the applied displacement \(\delta\) in Fig.  9 .

The force–displacement curve of inclined beams depicting negative stiffness region in segment BD.

The force–displacement curve is analyzed in three distinct segments:

Segment AB represents the initial positive stiffness linear region, triggered by the initial buckling of the beam.

Segment BD represents the linear negative stiffness region, induced by the snap-through behavior of the inclined beam during buckling.

Segment DE depicts the linear positive stiffness region post-buckling of the beam.

It is also noted that point C represents the unstable equilibrium point of the beam, where the axial reaction force is zero. As discussed in section " Mechanism behind the structure ", at this equilibrium point, the external force is completely supported by the in-plane lateral force of the beams.

The segment BD is the working region for the proposed design, as this segment exhibits an excellent negative stiffness region. The negative stiffness can be calculated as the slope of segment BD:

If the obtained negative stiffness region is connected in parallel to the equivalent positive stiffness region, then a quasi-zero stiffness region can be achieved. Therefore, the semicircular arch should be designed to exhibit positive linear stiffness of magnitude \(2{k}_{s}=0.13711\) N/mm. Here, \(2{k}_{s}\) is considered because the stiffness expression in Eq. ( 30 ) is for a single semicircular arch. Consequently, the parameters required to design the semicircular arch are reported in Table 3 (calculated from Eq. ( 30 )). The width and Young’s modulus are considered the same as those of the inclined beams. The force–displacement curve obtained from Eq.  30 is shown in Fig.  10 , where \(2{k}_{s}\) represents the slope of the designed semi-circular arch.

Force–displacement curve of semi-circular arch depicting stiffness \({k}_{s}\) .

The parallel springs theory states that the equivalent stiffness is the sum of the stiffness of individual springs connected in parallel. Hence, the equivalent stiffness for a unit cell \({k}_{eq-uc}\) is expressed as:

Substituting the values of \({k}_{b}\) (from Eq. ( 31 )) and \({k}_{s}\) (from Eq. ( 30 )) and using the parameters mentioned in Table 3 into Eq. ( 32 ), we obtain:

It can be observed from Eq. ( 33 ) that an almost zero-equivalent stiffness is achieved for the unit cell in segment BD (Fig.  9 ). As a result, the distance between B and D can be defined as the quasi-zero-stiffness region.

To obtain the force–displacement relation for the unit cell \({F}_{eq-uc}\) , the reaction force value of the beam \({F}_{b}\) and arches \({F}_{s}\) can be calculated for a displacement \(\delta\) as follows:

The force–displacement curve of the unit cell is illustrated in Fig.  11 . Within the segment BD, a quasi-zero-stiffness (QZS) region is observed, where the reaction force remains constant despite increasing displacement. Conversely, segments AB and DE display a linear stiffness behavior.

The force–displacement curve of unit cell obtained from analytical model.

To further enhance the design, a metastructure is configured by arranging four unit cells in a parallel orientation. According to parallel spring theory, the equivalent stiffness of the metastructure is the sum of the stiffness of each unit cell when subjected to a uniform load. Consequently, the relationships for stiffness-displacement and force–displacement for the metastructure can be described as follows:

In the above, \({k}_{eq-ms}\) and \({F}_{eq-ms}\) represent the equivalent stiffness and force of the metastructure, respectively. The static behavior of the proposed model is further explored both experimentally and numerically in the subsequent section.

Static characteristics

The quasi-zero-stiffness (QZS) behavior of the designed model is based on the High Static and Low Dynamic (HSLDS) mechanism, which allows for significant load-bearing capacity while simultaneously exhibiting approximately zero-stiffness due to imposed geometrical nonlinearity in the form of nonlinear stiffness. This section examines these static characteristics through numerical and analytical studies and corroborates them with experimental results.

Fabrication of samples using a 3D printing technique

In this study, three distinct samples were fabricated to demonstrate different aspects of the design: (i) an inclined beam showing negative stiffness, (ii) a unit cell composed of an inclined beam and semicircular arches that exhibit QZS, and (iii) a metastructure also demonstrating QZS. These samples are fabricated based on the parameters delineated in Tables 1 and 3 . The fabrication employs the additive manufacturing method (3D printing), specifically the Fused Deposition Modeling (FDM) technique, which includes the following printing specifications: an infill density of 100%, a hexagonal infill pattern, a layer height of 0.1 mm, a nozzle diameter of 0.3 mm, and a base print speed of 2 mm/s.

The samples are depicted in Fig.  12 . The black material used is Thermoplastic Polyurethane (TPU), which is known for its elasticity and high toughness, making it a significant engineering material widely utilized in industrial applications. The orange material is Polylactic Acid (PLA), which behaves more plastically and is utilized here as stiff walls providing base support. The components were printed separately using both materials and subsequently assembled for experimental testing.

3D printed sample.

Numerical simulations

In this work, the designs are modeled in SOLIDWORKS 2020®, and Finite Element Analysis (FEA) is conducted using ANSYS 2021R® simulation software to examine the mechanical behavior of the proposed inclined beam, unit cell, and metastructure. The static behavior is analyzed within the static structural module, where meshing is performed using tetrahedral elements. A mesh convergence study is also conducted to ensure the accuracy of the analysis. Given the buckling behavior of the beam under deformation, re-meshing criteria are adopted to facilitate the study of the nonlinear behavior of the models.

To replicate the real-time experimental conditions, the base of the sample is fixed in all six degrees of freedom, including three translational and three rotational. The top plate is restricted to five degrees of freedom, permitting only downward translational motion. A quasi-static downward vertical displacement is applied using a step size approach, and large deflection settings are enabled to capture the nonlinear behavior and identify the buckling modes of the inclined beam. The boundary conditions are illustrated in Fig.  13 .

Finite element model of unit cell representing boundary conditions.

Quasi-static experiments

The compression experiment is conducted using a uniaxial tensile testing machine, applying displacement at a controlled strain rate of 1 mm/min. The static behavior of the samples is recorded in the force–displacement curve, and the buckling mode shapes are captured using cameras.

Results and discussion

This section explores the static behavior of the inclined beam, unit cell, and metastructure through analytical, numerical, and experimental methods. The results are analyzed based on the force–displacement curve, stiffness-displacement curve, and the response of the samples to different mode shapes under various vertical displacements.

The static behavior of the inclined beam under vertical displacement is analyzed in Fig.  14 ; the analytical results are derived from Eq. ( 29 ) (discussed in section " Analytical modeling of the inclined beam and semicircular arch "), while the numerical results are sourced from the simulation methodology (discussed in section " Numerical simulations "). These results are then corroborated with experimental outcomes. As shown in the experimental results of Fig.  14 , the reaction force increases to 0.20 N as the displacement rises from 0 to 1 mm, indicative of the initial buckling behavior of the inclined beam in the first mode shape. As the displacement extends from 1 to 3.9 mm, the inclined beam undergoes snap-through, leading to instability and a sudden decrease in reaction force from 0.20 to 0.025 N, marking a region of negative stiffness. As displacement continues to increase to 5 mm, the reaction force rises again as the inclined beam stabilizes in another stable state. Based on these force–displacement results, the force–displacement relation is established using the curve fit technique, and subsequently, the stiffness-displacement curve is plotted in Fig.  15 . The experimental curve demonstrates that as displacement increases, the stiffness decreases, and during the deflection range of 1 to 3.9 mm, the stiffness of the beam drops to a value of (−0.1) N/mm, representing the negative stiffness region, before increasing again.

Comparison of force–displacement curves obtained from analytical, numerical, and experimental for inclined beam.

Comparison of stiffness-displacement curves obtained from analytical, numerical, and experimental for inclined beam.

The numerical results align well with the experimental outcomes for both the force–displacement and stiffness-displacement curves, albeit some discrepancies are observed due to fabrication errors, since the sample is 3D printed in parts and subsequently assembled into a metastructure. For numerical simulations, the model is imported from SOLIDWORKS, whereas, for the experimental studies, the samples are 3D printed layer by layer, which could impact the behavior of the inclined beam. Analytical models also show reasonable agreement; however, deviations arise due to the assumptions made, such as considering fixed support for one end of the inclined beam and strictly axial deformation at the other end with the moving platform, which is challenging to replicate practically. Therefore, the developed analytical equations are valid under the specified conditions of the structure.

In the linear region of the force–displacement curve, the experimental and numerical results show good agreement, while the analytical results exhibit some variations. This discrepancy could be attributed to the use of the elliptical integral solution technique in the analytical study, which is employed to solve the general equation for post-buckling of beams considering large deformation. The elliptical integral solution provides a closed-loop solution that is effective for studying the linear negative stiffness region, a characteristic displayed by the inclined beam under vertical deformation. The solution also covers linear positive stiffness regions effectively.

A comparative analysis of the numerical and experimental responses of the inclined beam under vertical displacement is depicted in Fig.  16 . The behavior of the inclined beam is evident across different deformation modes:

Figure  16 a illustrates the initial condition of the inclined beam with no applied displacement.

Figure  16 b shows the buckling behavior during the snap-through, leading to negative stiffness with two inflection points, representing the two mode shapes of the beam. Symmetrical behavior is also noted for both inclined beams.

Figure  16 c displays the other stable state achieved due to the snap-through behavior. The numerical results correlate well with the observed experimental mode shapes.

Comparison of the behavior of inclined beam obtained from numerical and experimental results under different vertical displacements.

The static behavior of the unit cell under vertical displacement is detailed in Fig.  17 . The unit cell comprises inclined beams and semicircular arches to demonstrate QZS behavior. The analytical model is derived by solving Eq.  35 (see section " Mechanical model of the structure "), and the numerical simulation follows the methodology previously discussed. The experimental outcomes depicted in Fig.  17 are analyzed across three regions of the force–displacement curve:

The first region shows positive stiffness, where the force increases from 0 to 0.45 N as the displacement extends from 0 to 1.6 mm. During this phase, the beam starts exhibiting the first mode shape (referenced in Fig.  6 ) and demonstrates a positive stiffness region, while the semicircular arch undergoes bending and shows a linear positive stiffness.

The second region maintains the force constant at approximately 0.45 N from displacements ranging 1.6–3.9 mm, leading to a QZS region. The beam experiences snap-through, crosses the unstable equilibrium state, enters the second mode shape (noted in Fig.  6 ), and exhibits a negative stiffness region, while the arch continues to bend, showing positive stiffness, combining with the beam to exhibit a QZS region.

The third region starts from 3.9 to 5 mm displacement, where force increases from 0.6 to 0.7 N, representing a positive stiffness region. The beam, after snap-through, reaches another stable state and demonstrates positive stiffness, which, combined with the arch’s stiffness, presents a positive stiffness region.

Comparison of force–displacement curves obtained from analytical, numerical, and experimental for the unit cell.

The stiffness-displacement curve, shown in Fig.  18 , is derived by differentiating the force–displacement relation from Fig.  17 using a curve fitting method. It reveals that in the displacement range of 2 to 4 mm, the stiffness hovers around 0 N/mm, indicating the QZS region. Hence, the designed unit cell exhibits nonlinear static behavior under applied vertical force. Comparing analytical and numerical results with experimental data, it is evident that numerical results closely match the experimental findings, while analytical results, though near, show slight variations due to idealized conditions assumed in model formulations and potential material property alterations from 3D printing.

Comparison of stiffness-displacement curves obtained from analytical, numerical, and experimental for the unit cell.

Different mode shapes of the unit cell under vertical deformation during numerical simulation and experimental studies are captured and shown in Fig.  19 . Figure  19 a illustrates the initial condition of the unit cell with no applied displacement. As displacement increases, the inclined beam undergoes buckling and reaches the second mode shape with two inflection points (as shown in Fig.  19 b) during the snap-through, while the semicircular arch undergoes bending, observable in Fig.  19 b. With further increase in displacement, the beam goes through snap-through to reach another stable state (as shown in Fig.  19 c), and the semicircular arch exhibits further bending behavior to demonstrate positive stiffness. It is noted that the mode shapes obtained from numerical simulations align with those captured experimentally.

Comparison of the behavior of unit cell obtained from numerical and experimental results under different vertical displacements.

The unit cells are organized in parallel to form a metastructure that acts as a platform for supporting a mass and demonstrating quasi-zero-stiffness (QZS) characteristics. The proposed model utilizes the high static and low dynamic stiffness mechanism, as evidenced experimentally in Fig.  20 . The analytical curve is generated using Eq. ( 37 ), and numerical results are derived using the methodology discussed in section " Numerical simulations ".

Comparison of force–displacement curves obtained from analytical, numerical, and experimental for metastructure.

As shown in Fig.  20 , in the initial phase, with an increase in displacement from 0 to 1.9 mm, the force also increases from 0 to 1.45 N. This initial positive stiffness region provides high static stiffness to support a load of 1.45 N. As displacement increases from 1.9 to 3.9 mm, the metastructure enters a transition phase where the force remains approximately constant at 1.45 N, defining this as the quasi-zero stiffness region where dynamic stiffness is notably low (approximately zero). Due to vertical displacement, the beam buckles and undergoes snap-through, exhibiting negative stiffness, while the semicircular arch undergoes bending-dominated behavior and exhibits positive stiffness, effectively countering the negative stiffness to exhibit QZS. With a further increase in displacement to 5 mm, the force again increases to 3 N, indicating positive stiffness. The QZS region represents the primary functional range of the proposed model.

Based on the force–displacement results, the stiffness-displacement relation is derived using the curve fit technique, and the stiffness-displacement curve is plotted in Fig.  21 . In the displacement region from 1.9 to 3.9 mm, the obtained stiffness is approximately zero and is symmetric about a displacement of 2.9 mm. This symmetry indicates the positive linear stiffness regions before and after the QZS region. It is also noted that the analytical and numerical results align closely with the experimental findings. The analytical solution deviates somewhat due to the ideal conditions assumed in the model, such as fixed support at one end and strict axial deformation at the guided end. Furthermore, in the experimental setup, models are fabricated using two different materials and finally assembled, which may also influence the experimental outcomes.

Comparison of stiffness-displacement curves obtained from analytical, numerical, and experimental for metastructure.

The displacement behavior of the metastructure during the experiment and numerical simulations is captured and compared in Fig.  22 . Figure  22 a shows an isometric view of the proposed metastructure. As displacement increases, the transition zone from positive to quasi-zero stiffness is evident in Fig.  22 b, showcasing the second buckling mode shape of the inclined beam with two inflection points during the snap-through behavior, while the semicircular arch demonstrates bending behavior. The symmetric deformation of the beam and arch, indicative of the metastructure’s stability, represents the QZS region, which is the main working region of the proposed metastructure. Figure  22 c illustrates the other stable state of the inclined beam leading to the shift of metastructure stiffness from quasi-zero to positive.

Comparison of the behavior of metastructure obtained from numerical and experimental results under different vertical displacements.

The static analysis confirms that the proposed model under downward vertical displacement exhibits nonlinear static behavior based on the high static and low dynamic stiffness mechanism. Experimentally, a static stiffness of 137.11 N/m is achieved with a QZS payload of 1.45 N, resulting in a QZS region of 2 mm. These results validate the analytical and numerical predictions with experimental data. The obtained static results will serve as a basis for the dynamic behavior study in section " Dynamic characteristics ".

Dynamic characteristics

The static analysis results suggest that the proposed metastructure exhibits quasi-zero-stiffness characteristics under vertical deformation. The designated QZS region is where the dynamic stiffness of the system is low, corresponding to low natural frequencies. This section investigates the dynamic behavior of the model to assess the vibration isolation capabilities of the metastructure across low-frequency ranges. Both analytical and experimental methodologies are employed to examine the dynamic properties of the proposed system. The investigation begins with the formulation of a dynamic equation and its solution using the Harmonic Balance Method. Subsequently, experiments are conducted to evaluate the vibration isolation performance of the system.

Analytical modeling of dynamic equation

To study the dynamic equation for nonlinear isolators, it is better to convert the static relationship of the metastructure into a non-dimensional form. This is achieved by applying curve-fitting techniques to the experimental results displayed in Fig.  20 , using regression analysis. Figure  23 illustrates the curve-fit model employing both third-order and fifth-order polynomials. It can be shown that the fifth-order polynomial provides a closer fit to the experimental data, with an \({R}^{2}\) value nearing 1, compared to the third order. The obtained non-dimensional equation for the fifth order is expressed as:

Curve-fit of experimental data obtained in static analysis.

The equivalent spring-dashpot-mass model is shown in Fig.  24 . The mass is supported by a spring exhibiting nonlinear behavior and a viscous damper. Under a base excitation, the equation of motion of the system can be expressed as:

where \(X\) denotes the relative displacement between mass and base, \({F}_{qzs}\left(X\right)\) denotes the nonlinear static force in dimensional form, \(\ddot{Y={Y}_{0}\text{sin}(\omega t)}\) is the excitation acceleration applied at the base and \(c\) is the damping coefficient. Equation ( 39 ) can be non-dimensionalized by introducing the following constants and variables:

in which \({\omega }_{n}\) is the natural frequency of the equivalent linear model, \(x\) is the non-dimensional relative displacement, \(\xi\) is the damping ratio, \({y}_{0}\) is the non-dimensional excitation amplitude, \(\tau\) is the non-dimensional time, and \(\Omega\) is the frequency ratio. Substituting Eq. ( 40 ) into Eq. ( 39 ), the equation of motion can be rewritten in non-dimensional form:

Spring-mass model for the dynamic study.

The ( \({\prime}\) ) denotes the derivative with respect to the non-dimensional time \(\tau\) , \({f}_{qzs}\) is the non-dimensional force–displacement relation. Equation ( 41 ) represents the dynamic equation, which exhibits a steady-state vibration response around the static equilibrium position under small excitation amplitudes. This equation can also be articulated as a nonlinear dynamic equation. Solving this equation involves two components: a particular integral solution and free vibration. As damping is incorporated, the free vibration term diminishes over time. To solve the particular integral, various methods have been utilized by researchers—such as the perturbation method, method of multiple scales, averaging method, and harmonic balance method (HBM). Among these, HBM is particularly advantageous because it is not limited to only weakly nonlinear problems and can converge to an accurate periodic solution for nonlinear systems 97 . Carrella. A 98 applied HBM to address the nonlinear dynamic equation, noting that omitting higher order harmonic terms and presuming the response to be purely harmonic does not yield precise solutions to the duffing equation. However, when the linear term of the restoring force equation is more significant than the nonlinear term, using the first order harmonic balance method results in a reasonable approximate solution, particularly when the primary concern is the output response at the excitation frequency, as this simplifies the mathematical resolution 99 . One limitation of HBM is that it requires separate analysis to assess the system’s stability. In this study, HBM is employed to solve the nonlinear differential equation to derive the steady-state vibration response.

The single mode of Harmonic Balance can be expressed as:

\(A\) is the amplitude and \(\psi\) is the phase response. Substituting Eq. ( 42 ) into Eq. ( 41 ) and solving the eigenvalue problem we obtain:

The frequency response curve, depicted in Fig.  25 for varying excitation amplitudes and a constant damping ratio, demonstrates a slight rightward bend; this is attributed to the positive coefficient of cubic stiffness, indicating a hardening scenario. This bend exemplifies the jump phenomenon’s effect in the model. As the frequency ratio sweeps forward, a sudden drop in amplitude occurs after reaching the peak, denoting the jump-down of amplitude during the forward sweep. Conversely, during the backward sweep, a sudden increase in amplitude is noted, indicating the jump-up phenomenon during the reverse sweep. According to the observations from Fig.  25 , both jump-down and jump-up occur within the same frequency ratio range in the proposed model. The area between the jump-up and jump-down is considered unstable, due to the abrupt changes in amplitude that could potentially damage the system. Therefore, it is recommended that the system be designed for a frequency range extending beyond the jump-up and jump-down conditions.

Frequency response curve for varying excitation amplitude and constant damping ratio.

Figure  25 further reveals that with an increase in excitation amplitude, the curve shifts towards a higher frequency range, exhibits more bending, and the peak amplitude also increases. Conversely, a lower excitation amplitude demonstrates a better isolation range, suggesting that a system designed for low excitation amplitude is preferable for enhanced isolation performance. Figure  26 illustrates the frequency response of the system with a constant excitation amplitude and varying damping ratios. It is observed that as the damping decreases, the peak amplitude rises and the curve shifts to a higher frequency range with more pronounced bending. However, at high-frequency ratios, the system shows effective isolation performance across all damping ratios. Thus, the system should ideally be designed for low-excitation amplitude coupled with an optimal damping ratio to achieve superior vibration isolation performance in low-frequency ranges.

Frequency response curve for varying damping ratio and constant excitation amplitude.

Stability response of the system

An abrupt change in the structural response of the system by a small variation in any of its parameters is known as the unstable state of the system. In this section, the unstable region of the proposed model is studied by performing a stability analysis. The Harmonic Balance is used to solve the nonlinear dynamic equation. Therefore, the same will be used to find the steady-state response for the stability analysis. First, a non-dimensional perturbation parameter \(\sigma (\tau )\) is introduced and superimposed into Eq. ( 42 ):

Ignoring the terms of order higher than \(O({\sigma }^{2})\) and higher-order harmonics, the equation of motion in non-dimensional perturbation term can be expressed as:

The equation of motion outlined in Eq. ( 46 ) is referred to as the damped Mathew’s equation, where \(v\) is a function of \(w\) , and the plane \(( v-w )\) is divided into stable and unstable regions by the transition curve. This transition curve is derived by conducting a perturbation analysis. The solution to Eq. ( 48 ) delineates the transition curve as a parabolic equation:

The region enclosed by this parabolic curve, illustrated as a shaded area in Fig.  27 , represents instability. Observations from Fig.  27 indicate that the unstable region coincides with the bending region of the Frequency Response Function (FRF) curve, where the jump phenomenon is evident. Consequently, the unstable intermediate branch is situated between the jump-up and jump-down frequencies of the frequency response. To enhance system stability, it is advisable to design systems that avoid bending in the FRF curve.

Stability curve for \(\xi =0.05\) and \({y}_{0}=0.05\) .

A parametric study has also been conducted to examine how changes in the damping ratio and excitation amplitude affect the behavior of unstable regions. According to the results shown in Fig.  28 , increasing the damping leads to a reduction in the unstable region, thereby diminishing the bending and enhancing the system’s stability. Conversely, the stability response of the system appears to be independent of the excitation amplitude, indicating that changes in amplitude do not significantly impact the stability regions.

Parametric study for the unstable regions for varying damping ratios.

Experimental setup

Vibration shaker experiments were conducted to evaluate the dynamic behavior of the proposed model under various payloads. Three distinct payloads were chosen based on the static results displayed in Fig.  20 : (i) a mass in the QZS region, identified as QZS payload (185 g), (ii) a lighter payload of 145 g (less than the QZS payload), and (iii) a heavier payload of 225 g (more than the QZS payload). The experimental setup, depicted in Fig.  29 , involves the payload being mounted atop the metastructure, which in turn is connected to an electromagnetic shaker via a fixture. Signals are initially generated in the wave generator, subsequently amplified by the power amplifier, and then delivered as input to the shaker. An accelerometer is installed on top of the payload to capture the output signal, while a second accelerometer is affixed to the base plate to record the input signal. Both accelerometers are linked to a data acquisition system that gathers and analyzes the raw signals using T-Vib software. This setup allows for a detailed examination of the metastructure’s response to dynamic loads under different mass conditions.

Experimental setup to study dynamic behavior with metastructure fixed on the top of the shaker.

Vibration isolation performance

The key parameter to assess the vibration performance of the metastructure is the transmissibility response in steady state for specific frequency ranges. In this experimental setup, the base of the metastructure is mounted on the shaker, and base excitation is administered as an input in the form of sinusoidal waves. These waves pass through the metastructure and reach the top, where the output is measured. Under the influence of the payload, the metastructure serves as a vibration isolator. Transmissibility is calculated based on the ratio of time-domain data recorded at the top of the payload to that applied at the bottom for a designated frequency.

The dynamic behavior of the metastructure under a QZS payload is analyzed. A mass of 185 g is mounted on the top of the metastructure to deform it into the QZS region. Input and output acceleration readings are captured from the accelerometers installed on the bottom and top of the metastructure, respectively. The base is excited with a sinusoidal input acceleration represented by \({A}_{0}\text{sin}\omega t\) , where \({A}_{0}\) denotes the acceleration amplitude, \(\omega\) the excitation frequency, and \(t\) the time period of the excitation.

The base is subjected to a constant acceleration magnitude while the frequency varies from 5 to 35 Hz. The step size is set at 1 Hz from 5–17 Hz and 19–35 Hz, and at 0.5 Hz between 17 and 19 Hz. Time-domain data are recorded for each frequency, and the root mean square (rms) value of the amplitude is calculated at both input and output. The transmissibility in decibels is then determined by the formula:

Figure  30 a–d illustrates the time response for certain frequencies under a QZS payload of 185 gm, where the black dotted line indicates the input and the red solid line represents the output. It is noticeable that at a frequency of 10 Hz, the output magnitude exceeds that of the input. As the frequency increases to 18 Hz, the output amplitude reaches its maximum value. Upon further increment to 18.5 Hz, a sudden drop in the output amplitude is observed, and by the frequency of 25 Hz, the output amplitude significantly reduces compared to the input, demonstrating effective isolation.

The time domain response of QZS region payload (185 gm) for different excitation frequencies.

Based on the time response data obtained, transmissibility is calculated using Eq. ( 49 ) and plotted against each frequency in Fig.  31 . It is noticeable that as the frequency increases from 5 Hz, the transmissibility correspondingly rises until it reaches a peak value of 9 dB at 18 Hz. With an incremental frequency increase to 18.5 Hz, the transmissibility sharply drops to −4 dB. This sudden change in transmissibility from 9 to −4 dB within a narrow frequency range of 0.5 Hz exemplifies what is technically known as the jump phenomenon. As the frequency continues to increase from 18.5 to 35 Hz, the transmissibility further declines to -13.5 dB, indicating that the isolation range of the metastructure under QZS load begins for frequencies higher than 18.5 Hz.

Transmissibility vs. frequency response of the QZS payload (185 gm).

To explore the jump phenomenon, a sine sweep from 3 to 23 Hz over a period of 20 s was conducted. A forward sweep is utilized to examine the jump-down phenomenon, and a backward sweep is used to analyze the jump-up phenomenon. Observations from Fig.  32 a reveal that as the frequency increases, the amplitude also increases until it reaches its peak. With a further rise in frequency, a noticeable jump-down in amplitude occurs; this denotes a rapid transition from the resonance peak to the isolation region. This abrupt decrease in amplitude from 18 to 18.5 Hz is also evident in Fig.  33 a. Conversely, during the backward sweep, as shown in Fig.  32 b, when the frequency decreases, the amplitude rises, and a sudden jump-up is noted, indicating a swift transition from the isolation region back to a region of higher amplitude. This sudden increase in amplitude from 18.5 to 18 Hz is similarly reflected in Fig.  33 b. The overlap of forward and backward sweeps is also depicted in Fig.  32 c, illustrating the dynamic shifts in amplitude associated with different sweep directions.

Represents the time vs. amplitude response of the QZS payload under sine sweep from 4 to 23 Hz for 20 s. ( a ) forward sweep response, ( b ) backward sweep response. ( c ) superposition of forward and backward response.

Captured time domain response during the transition of frequency ( a ) from 18 to 18.5 Hz, ( b ) from 18.5 to 18 Hz.

Parametric study

Two parametric studies were conducted to experimentally evaluate the dynamic performance of the designed metastructure: (i) under varying payloads mounted on the top of the metastructure and (ii) under varying excitation amplitudes.

Three different payloads are selected based on the force–displacement curve presented in Fig.  20 . The first payload, weighing 145 g, is chosen from the positive stiffness region and is lighter than the QZS payload. The second payload, weighing 185 gm, is the QZS payload selected from the QZS region. The third payload, weighing 225 g, is heavier than the QZS payload and is also selected from the positive stiffness region.

In the parametric study involving different payloads, the first and third payloads were mounted on the shaker, and base excitation was applied from the bottom with the same amplitude used for the QZS payload and over the same frequency range. The time response under various frequencies was then recorded and displayed in Fig.  34 a–d for the 145 g mass and in Fig.  35 a–d for the 225 g mass. Transmissibility was calculated from the RMS values measured at the top and bottom for each frequency and plotted in Fig.  36 .

The time domain response of linear stiffness region payload (145 gm) for different excitation frequencies.

The time domain response of linear stiffness region payload (225 gm) for different excitation frequencies.

Parametric study of the transmissibility vs. frequency curve for three different weights. QZS payload mass- 185 gm, Linear stiffness region mass- 145 gm, Linear stiffness region mass- 225 gm.

Figure  36 shows that as the frequency increases, transmissibility also increases for all three payloads. As frequency further increases, the 145 g payload reaches a peak transmissibility of 12 dB at 22.5 Hz, then the transmissibility starts decreasing, and isolation begins at 26.3 Hz. The QZS payload reaches a peak transmissibility of 9 dB at 18 Hz, with isolation starting at 18.5 Hz. The 225 g payload reaches a peak transmissibility of 10.75 dB at 20 Hz, with isolation beginning at 24 Hz. These observations indicate that for linear payload masses, the system exhibits linear behavior. In contrast, for the payload designed in the QZS region, the system shows nonlinear behavior, where effective vibration isolation starts from 18.5 Hz, and resonance occurs at 18 Hz with a peak value of 9 dB, which is the lowest compared to the other two masses. At higher frequencies, the QZS payload demonstrates better isolation performance than the other two masses.

The results of the parametric study, including transmissibility peak value, resonance frequency, and isolation frequency, are plotted in the bar chart of Fig.  37 a, Fig.  37 b and Fig.  37 c respectively. The quantitative comparison is performed based on two cases: (i) vibration performance between two linear stiffness region masses (145 g and 225 g), and (ii) vibration performance between a quasi-zero-stiffness region mass (185 g) and a linear stiffness region mass (225 g). For the first case, it can be observed that the 145 g mass exhibits a higher transmissibility peak value (12 dB) and at a higher resonance frequency (26.3 Hz) than the 225 g mass, which shows a peak of 10.75 dB at 24 Hz; also, the isolation of the 145 g mass starts at a higher frequency compared to the 225 gm. This comparison suggests that both masses behave linearly, and for vibration isolation in a low-frequency range, a heavier mass (i.e., 225 g) is preferable. For the second case, the 185 g mass shows a lower transmissibility peak value (9 dB) and at a lower resonance frequency (18 Hz) than the 225 g mass, which exhibits a peak of 10.75 dB at 24 Hz; also, the isolation of the 185 g mass starts at a lower frequency compared to the 225 g mass. This comparison does not follow a linear trend, and for vibration isolation in the low-frequency range, a lower mass (185 g-QZS payload) is appropriate. These comparisons validate that the proposed metastructure exhibits nonlinear behavior and can effectively isolate vibrations at low-frequency ranges when designed for the QZS payload.

Qualitative comparison of the vibration performance of three different payloads achieved experimentally, (i) transmissibility peak value, (ii) resonance frequency, (iii) isolation region starts.

For the parametric study focusing on different excitation amplitudes, the payloads are mounted on the shaker, and their transmissibility was calculated for two distinct excitation amplitudes, with results plotted against the frequency in Fig.  38 . Observations from Fig.  38 a reveal that the QZS payload displays nonlinear behavior (jump phenomenon) under both high and low amplitude excitations. Notably, lower excitation amplitude results in superior isolation performance at lower frequencies. However, at higher frequency ranges, similar isolation performance is noted across both excitation amplitudes. Conversely, for the other two masses, as depicted in Fig.  38 b, c, low amplitude excitation provides better isolation performance at lower frequencies, while high amplitude excitation yields improved isolation performance at higher frequencies, indicating that these payloads behave linearly.

Parametric study of transmissibility vs. frequency curve under low and high excitation amplitude for three different masses- ( a ) QZS payload mass- 185 gm, ( b ) Linear stiffness region mass- 145 gm, ( c ) Linear stiffness region mass- 225 gm.

The dynamic study highlights that the developed metastructure exhibits nonlinear behavior (jump phenomenon) within the QZS region and achieves better isolation performance, lower peak values, and lower resonance frequencies with the QZS payload compared to the other payloads. This distinction proves the unique capabilities of the QZS design in enhancing vibrational isolation, particularly in scenarios where minimizing the transmission of vibrations is critical.

Conclusions

In this study, a vibration isolator is designed to exhibit Quasi-Zero-Stiffness (QZS) characteristics, with its static and dynamic performances investigated analytically and subsequently validated using experimental results. The metastructure is conceived based on the High Static and Low Dynamic Stiffness (HSLDS) mechanism, integrating elements of negative stiffness with those of positive stiffness. The architecture of the proposed metastructure comprises four unit cells arranged in parallel, where each unit cell consists of inclined beams and semicircular arches. Under vertical compression, the inclined beams exhibit negative stiffness as they undergo buckling and snap-through behaviors, while the semicircular arches, undergoing bending-dominated behavior, provide positive stiffness to counterbalance the negative effects and achieve the QZS characteristics.

The design procedure of the inclined beams and arches was analyzed by considering large deformation scenarios to assess the buckling behavior of the beams, and the parameters for the semicircular arches were tailored based on the derived negative stiffness. Subsequently, samples were fabricated using 3D printing techniques. The static behaviors of the inclined beam, unit cell, and the entire metastructure were thoroughly investigated using analytical and numerical methods via ANSYS® software, and these findings were verified by laboratory tests. Moreover, the multiple loading cycle effect to analyze the fatigue life behavior of proposed metastructure is considered as a future scope of the work.

Building upon the static findings, the dynamic performance of the metastructure was investigated. An approximate nonlinear dynamic equation was formulated via curve fitting and solved using the Harmonic Balance method to describe the frequency response curve under varying frequency ratios. Vibration shaker experiments were conducted to assess the performance of the metastructure when loaded with the QZS payload. The transmissibility curve showed a jump-down phenomenon, confirming the nonlinear behavior of the proposed model. A comprehensive parametric study was carried out to evaluate the transmissibility behavior under three distinct payloads and various excitation amplitudes.

From the analytical, numerical, and experimental studies, it was shown that the proposed model not only represents QZS characteristics but also delivers effective vibration isolation performance, particularly within low-frequency ranges. This demonstrates the metastructure’s capability to mitigate vibrational impacts through innovative design and strategic material utilization, hence, establishing its potential applicability in practical engineering solutions where vibration isolation is critical.

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Preumont, A. Vibration Control of Active Structures. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72296-2

Carta, G., Movchan, A. B., Argani, L. P. & Bursi, O. S. Quasi-periodicity and multi-scale resonators for the reduction of seismic vibrations in fluid-solid systems. Int. J. Eng. Sci. 109 , 216–239. https://doi.org/10.1016/j.ijengsci.2016.09.010 (2016).

Article   CAS   Google Scholar  

Hou, W., Chang, J., Wang, Y., Kong, C. & Bao, W. Experimental study on the forced oscillation of shock train in an isolator with background waves. Aerosp. Sci. Technol. 106 , 106129. https://doi.org/10.1016/j.ast.2020.106129 (2020).

Article   Google Scholar  

Lee, W. B., Cheung, C. F. & To, S. Materials induced vibration in ultra-precision machining. J. Mater. Process. Technol. 89–90 , 318–325. https://doi.org/10.1016/S0924-0136(99)00146-6 (1999).

Rakheja, S., Wu, J. Z., Dong, R. G., Schopper, A. W. & Boileau, P. É. Comparison of biodynamic models of the human hand-arm system for applications to hand-held power tools. J. Sound Vib. 249 , 55–82. https://doi.org/10.1006/jsvi.2001.3831 (2002).

Article   ADS   Google Scholar  

Jiao, X., Zhang, J., Yan, Y. & Zhao, H. Research on nonlinear stiffness and damping of bellows-type fluid viscous damper. Nonlinear Dyn. 103 , 215–237. https://doi.org/10.1007/s11071-020-06146-9 (2021).

Gatti, G. Optimizing elastic potential energy via geometric nonlinear stiffness. Commun. Nonlinear Sci. Numer. Simul. 103 , 106035. https://doi.org/10.1016/j.cnsns.2021.106035 (2021).

Article   MathSciNet   Google Scholar  

Virgin, L. N., Santillan, S. T. & Plaut, R. H. Vibration isolation using extreme geometric nonlinearity. J. Sound Vib. 315 , 721–731. https://doi.org/10.1016/j.jsv.2007.12.025 (2008).

Sun, J., Huang, X., Liu, X., Xiao, F. & Hua, H. Study on the force transmissibility of vibration isolators with geometric nonlinear damping. Nonlinear Dyn. 74 , 1103–1112. https://doi.org/10.1007/s11071-013-1027-0 (2013).

Wang, S., Zhang, Y., Guo, W., Pi, T. & Li, X. Vibration analysis of nonlinear damping systems by the discrete incremental harmonic balance method. Nonlinear Dyn. 111 , 2009–2028. https://doi.org/10.1007/s11071-022-07953-y (2023).

Bian, J. & Jing, X. Superior nonlinear passive damping characteristics of the bio-inspired limb-like or X-shaped structure. Mech. Syst. Signal Process. 125 , 21–51. https://doi.org/10.1016/j.ymssp.2018.02.014 (2019).

Balaji, P. S. & Karthik SelvaKumar, K. Applications of nonlinearity in passive vibration control: a review. J. Vib. Eng. Technol. 9 , 183–213. https://doi.org/10.1007/s42417-020-00216-3 (2021).

Dalela, S., Balaji, P. S. & Jena, D. P. A review on application of mechanical metamaterials for vibration control. Mech. Adv. Mater. Struct. 29 , 3237–3262. https://doi.org/10.1080/15376494.2021.1892244 (2022).

Ibrahim, R. A. Recent advances in nonlinear passive vibration isolators. J. Sound Vib. 314 , 371–452. https://doi.org/10.1016/j.jsv.2008.01.014 (2008).

Wang, K. et al. A nonlinear ultra-low-frequency vibration isolator with dual quasi-zero-stiffness mechanism. Nonlinear Dyn. 101 , 755–773. https://doi.org/10.1007/s11071-020-05806-0 (2020).

Dalela, S., Balaji, P. S. & Jena, D. P. Design of a metastructure for vibration isolation with quasi-zero-stiffness characteristics using bistable curved beam. Nonlinear Dyn. 108 , 1931–1971. https://doi.org/10.1007/s11071-022-07301-0 (2022).

Ding, H. & Chen, L. Q. Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dyn. 95 , 2367–2382. https://doi.org/10.1007/s11071-018-4697-9 (2019).

Huang, X., Liu, X. & Hua, H. On the characteristics of an ultra-low frequency nonlinear isolator using sliding beam as negative stiffness. J. Mech. Sci. Technol. 28 , 813–822. https://doi.org/10.1007/s12206-013-1205-5 (2014).

Fulcher, B. A., Shahan, D. W., Haberman, M. R., Seepersad, C. C. & Wilson, P. S. Analytical and experimental investigation of buckled beams as negative stiffness elements for passive vibration and shock isolation systems. J. Vib. Acoust. Trans. ASME https://doi.org/10.1115/1.4026888 (2014).

Liu, C. & Yu, K. Accurate modeling and analysis of a typical nonlinear vibration isolator with quasi-zero stiffness. Nonlinear Dyn. 100 , 2141–2165. https://doi.org/10.1007/s11071-020-05642-2 (2020).

Kovacic, I., Brennan, M. J. & Waters, T. P. A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. J. Sound Vib. 315 , 700–711. https://doi.org/10.1016/j.jsv.2007.12.019 (2008).

Bouna, H. S., Nbendjo, B. R. N. & Woafo, P. Isolation performance of a quasi-zero stiffness isolator in vibration isolation of a multi-span continuous beam bridge under pier base vibrating excitation. Nonlinear Dyn. 100 , 1125–1141. https://doi.org/10.1007/s11071-020-05580-z (2020).

Liu, C. & Yu, K. Design and experimental study of a quasi-zero-stiffness vibration isolator incorporating transverse groove springs. Arch. Civ. Mech. Eng. 20 , 67. https://doi.org/10.1007/s43452-020-00069-3 (2020).

Zhao, F., Ji, J., Ye, K. & Luo, Q. An innovative quasi-zero stiffness isolator with three pairs of oblique springs. Int. J. Mech. Sci. 192 , 106093. https://doi.org/10.1016/j.ijmecsci.2020.106093 (2021).

Lan, C. C., Yang, S. A. & Wu, Y. S. Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads. J. Sound Vib. 333 , 4843–4858. https://doi.org/10.1016/j.jsv.2014.05.009 (2014).

Zhao, F., Ji, J. C., Ye, K. & Luo, Q. Increase of quasi-zero stiffness region using two pairs of oblique springs. Mech. Syst. Signal Process. 144 , 106975. https://doi.org/10.1016/j.ymssp.2020.106975 (2020).

Sun, X., Wang, F. & Xu, J. Analysis, design and experiment of continuous isolation structure with Local Quasi-Zero-Stiffness property by magnetic interaction. Int. J. Non. Linear. Mech. 116 , 289–301. https://doi.org/10.1016/j.ijnonlinmec.2019.07.008 (2019).

Zhou, Y., Chen, P. & Mosqueda, G. Analytical and numerical investigation of quasi-zero stiffness vertical isolation system. J. Eng. Mech. https://doi.org/10.1061/(asce)em.1943-7889.0001611 (2019).

Wang, L. et al. Ultra-low frequency vibration control of urban rail transit: the general quasi-zero-stiffness vibration isolator. Veh. Syst. Dyn. 60 , 1788–1805. https://doi.org/10.1080/00423114.2021.1874428 (2022).

Deng, Z. & Dapino, M. J. Review of magnetostrictive materials for structural vibration control. Smart Mater. Struct. 27 , 113001. https://doi.org/10.1088/1361-665X/aadff5 (2018).

Wang, K., Zhou, J., Wang, Q., Ouyang, H. & Xu, D. Low-frequency band gaps in a metamaterial rod by negative-stiffness mechanisms: Design and experimental validation. Appl. Phys. Lett. 114 , 251902. https://doi.org/10.1063/1.5099425 (2019).

Article   ADS   CAS   Google Scholar  

Li, M., Cheng, W. & Xie, R. Design and experiments of a quasi–zero-stiffness isolator with a noncircular cam-based negative-stiffness mechanism, JVC/Journal Vib. Control 26 , 1935–1947. https://doi.org/10.1177/1077546320908689 (2020).

Li, M., Cheng, W. & Xie, R. A quasi-zero-stiffness vibration isolator using a cam mechanism with user-defined profile. Int. J. Mech. Sci. 189 , 105938. https://doi.org/10.1016/j.ijmecsci.2020.105938 (2021).

Zhou, J., Wang, X., Xu, D. & Bishop, S. Nonlinear dynamic characteristics of a quasi-zero stiffness vibration isolator with cam-roller-spring mechanisms. J. Sound Vib. 346 , 53–69. https://doi.org/10.1016/j.jsv.2015.02.005 (2015).

Wang, F., Sun, X., Meng, H. & Xu, J. Tunable broadband low-frequency band gap of multiple-layer metastructure induced by time-delayed vibration absorbers. Nonlinear Dyn. 107 , 1903–1918. https://doi.org/10.1007/s11071-021-07065-z (2022).

Liu, S., Peng, G. & Jin, K. Design and characteristics of a novel QZS vibration isolation system with origami-inspired corrector. Nonlinear Dyn. 106 , 255–277. https://doi.org/10.1007/s11071-021-06821-5 (2021).

Zhou, J., Pan, H., Cai, C. & Xu, D. Tunable ultralow frequency wave attenuations in one-dimensional quasi-zero-stiffness metamaterial. Int. J. Mech. Mater. Des. 17 , 285–300. https://doi.org/10.1007/s10999-020-09525-7 (2021).

Ji, J. C., Luo, Q. & Ye, K. Vibration control based metamaterials and origami structures: A state-of-the-art review. Mech. Syst. Signal Process. 161 , 107945. https://doi.org/10.1016/j.ymssp.2021.107945 (2021).

Cai, C. et al. Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps. Compos. Struct. 236 , 111862. https://doi.org/10.1016/j.compstruct.2020.111862 (2020).

Meng, L., Sun, J. & Wu, W. Theoretical design and characteristics analysis of a quasi-zero stiffness isolator using a disk spring as negative stiffness element. Shock Vib. 2015 , 1–19. https://doi.org/10.1155/2015/813763 (2015).

Feng, X. & Jing, X. Human body inspired vibration isolation: Beneficial nonlinear stiffness, nonlinear damping & nonlinear inertia. Mech. Syst. Signal Process. 117 , 786–812. https://doi.org/10.1016/j.ymssp.2018.08.040 (2019).

Sun, X., Jing, X., Xu, J. & Cheng, L. Vibration isolation via a scissor-like structured platform. J. Sound Vib. 333 , 2404–2420. https://doi.org/10.1016/j.jsv.2013.12.025 (2014).

Wu, Z., Jing, X., Sun, B. & Li, F. A 6DOF passive vibration isolator using X-shape supporting structures. J. Sound Vib. 380 , 90–111. https://doi.org/10.1016/j.jsv.2016.06.004 (2016).

Vo, N. Y. P. & Le, T. D. Dynamic analysis of quasi-zero stiffness pneumatic vibration isolator. Appl. Sci. 12 , 2378. https://doi.org/10.3390/app12052378 (2022).

Palomares, E., Nieto, A. J., Morales, A. L., Chicharro, J. M. & Pintado, P. Numerical and experimental analysis of a vibration isolator equipped with a negative stiffness system. J. Sound Vib. 414 , 31–42. https://doi.org/10.1016/j.jsv.2017.11.006 (2018).

Carrella, A., Brennan, M. J. & Waters, T. P. Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 301 , 678–689. https://doi.org/10.1016/j.jsv.2006.10.011 (2007).

Carrella, A., Brennan, M. J., Kovacic, I. & Waters, T. P. On the force transmissibility of a vibration isolator with quasi-zero-stiffness. J. Sound Vib. 322 , 707–717. https://doi.org/10.1016/j.jsv.2008.11.034 (2009).

Carrella, A., Brennan, M. J., Waters, T. P. & Lopes, V. Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. Int. J. Mech. Sci. 55 , 22–29. https://doi.org/10.1016/j.ijmecsci.2011.11.012 (2012).

Gatti, G. Statics and dynamics of a nonlinear oscillator with quasi-zero stiffness behaviour for large deflections. Commun. Nonlinear Sci. Numer. Simul. 83 , 105143. https://doi.org/10.1016/j.cnsns.2019.105143 (2020).

Le, T. D. & Ahn, K. K. Experimental investigation of a vibration isolation system using negative stiffness structure. Int. J. Mech. Sci. 70 , 99–112. https://doi.org/10.1016/j.ijmecsci.2013.02.009 (2013).

Huang, X., Liu, X., Sun, J., Zhang, Z. & Hua, H. Vibration isolation characteristics of a nonlinear isolator using euler buckled beam as negative stiffness corrector: A theoretical and experimental study. J. Sound Vib. 333 , 1132–1148. https://doi.org/10.1016/j.jsv.2013.10.026 (2014).

Huang, X., Chen, Y., Hua, H., Liu, X. & Zhang, Z. Shock isolation performance of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: Theoretical and experimental study. J. Sound Vib. 345 , 178–196. https://doi.org/10.1016/j.jsv.2015.02.001 (2015).

Shaw, A. D., Gatti, G., Gonçalves, P. J. P., Tang, B. & Brennan, M. J. Design and test of an adjustable quasi-zero stiffness device and its use to suspend masses on a multi-modal structure. Mech. Syst. Signal Process. 152 , 107354. https://doi.org/10.1016/j.ymssp.2020.107354 (2021).

Sun, X. & Jing, X. Multi-direction vibration isolation with quasi-zero stiffness by employing geometrical nonlinearity. Mech. Syst. Signal Process. 62 , 149–163. https://doi.org/10.1016/j.ymssp.2015.01.026 (2015).

Cheng, C., Li, S., Wang, Y. & Jiang, X. Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping. Nonlinear Dyn. 87 , 2267–2279. https://doi.org/10.1007/s11071-016-3188-0 (2017).

Lu, Z. Q., Brennan, M., Ding, H. & Chen, L. Q. High-static-low-dynamic-stiffness vibration isolation enhanced by damping nonlinearity. Sci. China Technol. Sci. 62 , 1103–1110. https://doi.org/10.1007/s11431-017-9281-9 (2019).

Zhou, J., Wang, K., Xu, D., Ouyang, H. & Fu, Y. Vibration isolation in neonatal transport by using a quasi-zero-stiffness isolator. JVC/J. Vib Control 24 , 3278–3291. https://doi.org/10.1177/1077546317703866 (2018).

Zheng, Y., Li, Q., Yan, B., Luo, Y. & Zhang, X. A Stewart isolator with high-static-low-dynamic stiffness struts based on negative stiffness magnetic springs. J. Sound Vib. 422 , 390–408. https://doi.org/10.1016/j.jsv.2018.02.046 (2018).

Wang, S., Xin, W., Ning, Y., Li, B. & Hu, Y. Design, experiment, and improvement of a quasi-zero-stiffness vibration isolation system. Appl. Sci. 10 , 2273. https://doi.org/10.3390/app10072273 (2020).

Zhao, J. et al. A novel electromagnet-based absolute displacement sensor with approximately linear quasi-zero-stiffness. Int. J. Mech. Sci. 181 , 105695. https://doi.org/10.1016/j.ijmecsci.2020.105695 (2020).

Yuan, S. et al. A tunable quasi-zero stiffness isolator based on a linear electromagnetic spring. J. Sound Vib. 482 , 115449. https://doi.org/10.1016/j.jsv.2020.115449 (2020).

Vo, N. Y. P., Nguyen, M. K. & Le, T. D. Analytical study of a pneumatic vibration isolation platform featuring adjustable stiffness. Commun. Nonlinear Sci. Numer. Simul. 98 , 105775. https://doi.org/10.1016/j.cnsns.2021.105775 (2021).

López-Martínez, J., García-Vallejo, D., Arrabal-Campos, F. M. & Garcia-Manrique, J. M. Design of three new cam-based constant-force mechanisms. J. Mech. Des. Trans. ASME https://doi.org/10.1115/1.4040174 (2018).

Ye, K., Ji, J. C. & Brown, T. A novel integrated quasi-zero stiffness vibration isolator for coupled translational and rotational vibrations. Mech. Syst. Signal Process. 149 , 107340. https://doi.org/10.1016/j.ymssp.2020.107340 (2021).

Article   PubMed   Google Scholar  

Liu, S., Peng, G., Li, Z., Li, W. & Sun, L. Low-frequency vibration isolation via an elastic origami-inspired structure. Int. J. Mech. Sci. 260 , 108622. https://doi.org/10.1016/j.ijmecsci.2023.108622 (2023).

Ye, K. & Ji, J. C. An origami inspired quasi-zero stiffness vibration isolator using a novel truss-spring based stack Miura-ori structure. Mech. Syst. Signal Process. 165 , 108383. https://doi.org/10.1016/j.ymssp.2021.108383 (2022).

Zeng, P., Yang, Y., Huang, L., Yin, L. & Liu, B. An origami-inspired quasi-zero stiffness structure for low-frequency vibration isolation. J. Vib. Eng. Technol. 11 , 1463–1475. https://doi.org/10.1007/s42417-022-00651-4 (2023).

Liu, W., Wu, L., Sun, J. & Zhou, J. Origami-inspired quasi-zero stiffness metamaterials for low-frequency multi-direction vibration isolation. Appl. Phys. Lett. https://doi.org/10.1063/5.0164777 (2023).

Niu, M. Q. & Chen, L. Q. Analysis of a bio-inspired vibration isolator with a compliant limb-like structure. Mech. Syst. Signal Process. 179 , 109348. https://doi.org/10.1016/j.ymssp.2022.109348 (2022).

Han, W. J., Lu, Z. Q., Niu, M. Q. & Chen, L. Q. Analytical and experimental investigation on a NiTiNOL circular ring-type vibration isolator with both stiffness and damping nonlinearities. J. Sound Vib. 547 , 117543. https://doi.org/10.1016/j.jsv.2022.117543 (2023).

Zhang, Q., Guo, D. & Hu, G. Tailored mechanical metamaterials with programmable quasi-zero-stiffness features for full-band vibration isolation. Adv. Funct. Mater. 31 , 2101428. https://doi.org/10.1002/adfm.202101428 (2021).

Liu, C. H., Hsu, M. C., Chen, T. L. & Chen, Y. Optimal design of a compliant constant-force mechanism to deliver a nearly constant output force over a range of input displacements. Soft Robot. 7 , 758–769. https://doi.org/10.1089/soro.2019.0122 (2020).

Guo, L., Wang, X., Fan, R. L. & Bi, F. Review on development of high-static-low-dynamic-stiffness seat cushion mattress for vibration control of seating suspension system. Appl. Sci. 10 , 2887. https://doi.org/10.3390/APP10082887 (2020).

Liu, C. et al. Nonlinear dynamics of a magnetic vibration isolator with higher-order stable quasi-zero-stiffness. Mech. Syst. Signal Process. 218 , 111584. https://doi.org/10.1016/j.ymssp.2024.111584 (2024).

Liu, C., Zhao, R., Yu, K. & Liao, B. In-plane quasi-zero-stiffness vibration isolator using magnetic interaction and cables: Theoretical and experimental study. Appl. Math. Model. 96 , 497–522. https://doi.org/10.1016/j.apm.2021.03.035 (2021).

Yan, B., Yu, N. & Wu, C. A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms. Appl. Math. Mech. (English Ed.) 43 , 1045–1062. https://doi.org/10.1007/s10483-022-2868-5 (2022).

Kamaruzaman, N. A., Robertson, W. S. P., Ghayesh, M. H., Cazzolato, B. S. & Zander, A. C. Six degree of freedom quasi-zero stiffness magnetic spring with active control: Theoretical analysis of passive versus active stability for vibration isolation. J. Sound Vib. https://doi.org/10.1016/j.jsv.2021.116086 (2021).

Zhao, F., Ji, J. C., Cao, S., Ye, K. & Luo, Q. QZS isolators with multi-pairs of oblique bars for isolating ultralow frequency vibrations. Nonlinear Dyn. 112 , 1815–1842. https://doi.org/10.1007/s11071-023-09160-9 (2024).

Zheng, Y., Bin Shangguan, W., Yin, Z. & Liu, X. A. Design and modeling of a quasi-zero stiffness isolator for different loads. Mech. Syst. Signal Process. https://doi.org/10.1016/j.ymssp.2022.110017 (2023).

Kim, K. R., Han You, Y. & Ahn, H. J. Optimal design of a QZS isolator using flexures for a wide range of payload. Int. J. Precis. Eng. Manuf. 14 , 911–917. https://doi.org/10.1007/s12541-013-0120-0 (2013).

Liu, L., Chai, Y., Guo, Z. & Li, M. A novel isolation system with enhanced QZS properties for supporting multiple loads. Aerosp. Sci. Technol. 143 , 108719. https://doi.org/10.1016/j.ast.2023.108719 (2023).

Liu, C., Zhang, W., Yu, K., Liu, T. & Zheng, Y. Quasi-zero-stiffness vibration isolation: Designs, improvements and applications. Eng. Struct. 301 , 117282. https://doi.org/10.1016/j.engstruct.2023.117282 (2024).

Barchiesi, E., Spagnuolo, M. & Placidi, L. Mechanical metamaterials: a state of the art. Math. Mech. Solids 24 , 212–234. https://doi.org/10.1177/1081286517735695 (2019).

Frenzel, T., Findeisen, C., Kadic, M., Gumbsch, P. & Wegener, M. Tailored buckling microlattices as reusable light-weight shock absorbers. Adv. Mater. 28 , 5865–5870. https://doi.org/10.1002/adma.201600610 (2016).

Article   CAS   PubMed   Google Scholar  

Tan, X. et al. Reusable metamaterial via inelastic instability for energy absorption. Int. J. Mech. Sci. 155 , 509–517. https://doi.org/10.1016/j.ijmecsci.2019.02.011 (2019).

Ha, C. S., Lakes, R. S. & Plesha, M. E. Design, fabrication, and analysis of lattice exhibiting energy absorption via snap-through behavior. Mater. Des. 141 , 426–437. https://doi.org/10.1016/j.matdes.2017.12.050 (2018).

Zhao, J., Jia, N., He, X. & Wang, H. Post-buckling and snap-through behavior of inclined slender beams. J. Appl. Mech. Trans. ASME 75 , 0410201–0410207. https://doi.org/10.1115/1.2870953 (2008).

Howell, L. L. Compliant Mechanisms (2001).

Masters, N. D. & Howell, L. L. A self-retracting fully compliant bistable micromechanism. J. Microelectromech. Syst. 12 , 273–280. https://doi.org/10.1109/JMEMS.2003.811751 (2003).

Kim, C. & Ebenstein, D. Curve decomposition for large deflection analysis of fixed-guided beams with application to statically balanced compliant mechanisms. J. Mech. Robot. https://doi.org/10.1115/1.4007488 (2012).

Holst, G. L., Teichert, G. H. & Jensen, B. D. Modeling and experiments of buckling modes and deflection of fixed-guided beams in compliant mechanisms. J. Mech. Des. Trans. ASME https://doi.org/10.1115/1.4003922 (2011).

Ma, F. & Chen, G. Modeling large planar deflections of flexible beams in compliant mechanisms using chained beam-constraint-model. J. Mech. Robot. 8 , 55. https://doi.org/10.1115/1.4031028 (2016).

Chase, R. P., Todd, R. H., Howell, L. L. & Magleby, S. P. A 3-D chain algorithm with pseudo-rigid-body model elements. Mech. Based Des. Struct. Mach. 39 , 142–156. https://doi.org/10.1080/15397734.2011.541783 (2011).

Zhou, Z., Gao, Y., Sun, L., Dong, W. & Du, Z. A bistable mechanism with linear negative stiffness and large in-plane lateral stiffness: Design, modeling and case studies. Mech. Sci. 11 , 75–89. https://doi.org/10.5194/ms-11-75-2020 (2020).

Li, Y., Tijjani, M. Z., Jiang, X. & Ahmed, J. O. Band gap mechanism and vibration attenuation of a quasi-zero stiffness metastructure. Int. J. Struct. Integr. 13 , 1041–1059. https://doi.org/10.1108/IJSI-08-2022-0104 (2022).

Fan, H., Yang, L., Tian, Y. & Wang, Z. Design of metastructures with quasi-zero dynamic stiffness for vibration isolation. Compos. Struct. 243 , 112244. https://doi.org/10.1016/j.compstruct.2020.112244 (2020).

Peng, Z. K., Lang, Z. Q., Billings, S. A. & Tomlinson, G. R. Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis. J. Sound Vib. 311 , 56–73. https://doi.org/10.1016/j.jsv.2007.08.035 (2008).

Carrella, A. Passive vibration isolators with high-static-low-dynamic-stiffness, University of Southampton, 2008. https://eprints.soton.ac.uk/51276/ .

Brennan, M. J., Kovacic, I., Carrella, A. & Waters, T. P. On the jump-up and jump-down frequencies of the Duffing oscillator. J. Sound Vib. 318 , 1250–1261. https://doi.org/10.1016/j.jsv.2008.04.032 (2008).

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Acknowledgements

The author would like to thank the Department of Mechanical Engineering, National Institute of Technology Rourkela, for extending the facilities for this research. The authors are also thankful to the Dean of Scientific Research at King Khalid University and to the University of Sharjah.

This work is jointly supported by SERB, Department of Science and Technology, Govt. of India, under core research grant CRG/2021/002660 and by Dean of Scientific Research King Khalid University under grant number RGP2/345/45. Additional support was provided by the University of Sharjah, United Arab Emirates.

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Moussa Leblouba

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Suverna Trivedi

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S.D: Conceptualization, Investigation, Validation, Software, Data curation, Writing—original draft. P.S. B.: Methodology, Formal analysis, Writing—review & editing, Supervision, Project administration, Funding acquisition. M. L.: Funding acquisition; Writing—review and editing. S.V. and A.K. review ; Funding acquisition.

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Dalela, S., Balaji, P.S., Leblouba, M. et al. Nonlinear static and dynamic response of a metastructure exhibiting quasi-zero-stiffness characteristics for vibration control: an experimental validation. Sci Rep 14 , 19195 (2024). https://doi.org/10.1038/s41598-024-70126-x

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Published : 19 August 2024

DOI : https://doi.org/10.1038/s41598-024-70126-x

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